Week5/STA410_W24_Week5_Lecture_UsingLinearAlgebra.ipynb

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    "<a name=\"cell-solving\"></a>\n",
    "\n",
    "# 5. With great power comes great responsiblity: Using Linear Algebra for Good\n",
    "\n",
    "1. [Scaling / Artifical Ill-Conditioning](#cell-sovling-condition-artificial)\n",
    "2. [Multicollinearity and Variance Inflation Factors (VIFs)](#cell-sovling-Axb-math-multicollinearity)\n",
    "3. [Principal Components Analysis (PCA)](#cell-sovling-Axb-math-pca) [$X=UDV^T$](#cell-sovling-X-UDVt)\n",
    "    <!-- 1. [Why use PCA?](#cell-sovling-X-UDVt) -->\n",
    "    1. [SVD Versus Eigendecomposition for PCA (or PCR)](#cell-sovling-X-UDVt)\n",
    "    2. [Independent Components Analysis (ICA)](#cell-sovling-Axb-math-ica)\n",
    "4. [Principal Components Regression (PCR)](#cell-sovling-Axb-math-pcr)\n",
    "5. [$Ax=b\\;$in a few ways that aren't$\\;A^{-1}$](#cell-sovling-Axb)\n",
    "    1. [The return of the SVD](#cell-sovling-svd)\n",
    "    2. [The Cholesky](#cell-sovling-chol)\n",
    "    3. [Multivariate Normal](#cell-sovling-chol-mvn)\n",
    "    4. [Square Root Decomposition](#cell-sovling-mvn)\n",
    "    5. [$QR$ Decomposition](#cell-sovling-qr)\n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "\n"
   ]
  },
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   "source": [
    "# 5. With great power comes great responsiblity: Using Linear Algebra for Good\n",
    "\n",
    "Understanding <u>linear algebra</u> greatly clarifies both computational behavior and applied analysis\n",
    "\n",
    "- Magnitude differences in the ***singular values*** lead to ***numerical roundoff error*** \n",
    "- Magnitude differences in the ***singular values*** lead to an ***ill-conditioned*** matrix multiplication problem \n",
    "\n",
    "> The end of the previous `STA410_W24_Week4_Lecture_NumericalErrors.ipynb` notebook introduced ***singular value decomposition (SVD)*** and defined ***matrix condition number*** as the ratio of the largest to smallest ***singular values*** $\\frac{\\lambda_{\\max}}{\\lambda_{\\min}}$\n",
    "\n",
    "> See `STA410_W24_Extra_DerivingMatrixCondition.ipynb` for a formalization of the $\\frac{\\lambda_{\\max}}{\\lambda_{\\min}}$ ***matrix condition number*** as bounding the matrix multiplication problem's ***condition***\n",
    "\n",
    "\n",
    "- For a more general review of the core ***linear algebra*** concepts that we will continue to build upon in this current notebook, please review the again highly relevant `STA410_W24_Week4_Prerequesite_LinearAlgebra.ipynb` notebook \n"
   ]
  },
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   "source": [
    "<a name=\"cell-sovling-condition-artificial\"></a>\n",
    "\n",
    "# 5.1 Scaling / Artifical Ill-Conditioning ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "- $X$ will be ***ill-conditioned*** when column scales $X_{\\cdot i}$ and $X_{\\cdot j}$ are very different<br>$\\quad\\longrightarrow\\quad$ this causes the ***singular values*** $\\lambda_i$ and $\\lambda_j$ of the matrix (in ***SVD*** $X=UDV^T$) to have very different magnitudes\n",
    "\n",
    "- This is <u>***artifical ill-conditioning***</u> in the case of ***design matrix*** $X$<br>$\\quad\\longrightarrow\\quad$ the columns can just be rescaled to produced ***well-conditioned*** $\\tilde X$\n",
    "\n",
    "    > Remember the ever-present recommendation \"center and scale your data\" for regression?\n",
    "    > -  Or how $E[X^2]-E[X]^2$ variance calcultions can break on \"uncentered\" data \n",
    "    but would work just fine for \"centered\" data?\n",
    "    >\n",
    "    > Centering and scaling your data just fixes ***artifical ill-conditioning*** problems...\n",
    "\n",
    "<!-- This is because the sum of the ***singular values*** are [bounded](https://math.stackexchange.com/questions/1472420/upper-bound-for-the-sum-of-absolute-values-of-the-eigenvalues) by the sum of the elements of a matrix; thus,  -->\n",
    "\n",
    "<br><br><br>\n"
   ]
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   "source": [
    "<a name=\"cell-sovling-condition-artificial\"></a>\n",
    "\n",
    "# 5.1 Scaling / Artifical Ill-Conditioning ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "- $X$ will be ***ill-conditioned*** when ~~column~~ROW scales $X_{k\\cdot }$ and $X_{l\\cdot }$ are very different<br>$\\quad\\longrightarrow\\quad$ this causes the ***singular values*** $\\lambda_k$ and $\\lambda_l$ of the matrix (in ***SVD*** $X=UDV^T$) to have very different magnitudes\n",
    "\n",
    "- This is <u>***artifical ill-conditioning***</u> in the case of some ***matrix*** $X$<br>$\\quad\\longrightarrow\\quad$ the ~~columns~~ROWS can just be rescaled to produced ***well-conditioned*** $\\tilde X$\n",
    "\n",
    "***Multivariate first-order Taylor approximations*** to systems of nonlinear equations \n",
    "\n",
    "$$\\overset{\\text{nonlinear system}}{\\underset{\\text{of equations}}{b = f(x)}} \\approx \\underbrace{f(x^{(t)}) + \\overbrace{\\left[\\begin{array}{ccc}\\frac{\\partial f_1(x^{(t)})}{\\partial x_1} & \\cdots & \\frac{\\partial f_1(x^{(t)})}{\\partial x_p} \\\\\n",
    "\\vdots & \\ddots & \\vdots \\\\\n",
    "\\frac{\\partial f_n(x^{(t)})}{\\partial x_1} & \\cdots & \\frac{\\partial f_n(x^{(t)})}{\\partial x_p} \n",
    "\\end{array} \\right]}^{\\text{the Jacobian } J_{f(x)}(x^{(t)}) \\,=\\, \\nabla_{f(x)}(x^{(t)})^T}  (x-x^{(t)})}_{\\text{Approximated as a system of } \\underset{\\color{gray}{b \\,\\approx\\, f(x^{(t)})+  J_{f(x)}(x^{(t)} (x-x^{(t)})}}{\\text{linear equations }b \\,\\approx\\, c+Ax'}} \\quad \\begin{array}{l}\\text{can be rescaled, i.e., to $c_ib_i = c_if_i(x)$}\\\\\\text{(rescaling outcome variables of $f$)}\\\\\\text{to remove magnitude differences}\\\\\\text{between parital derivatives rows}\\\\\\text{so the }\\textbf{Jacobian}\\text{ is }\\textbf{well-conditioned}\\end{array}$$\n",
    "\n"
   ]
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   "source": [
    "<a name=\"cell-sovling-Axb-math-multicollinearity\"></a>\n",
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs) ([Return to TOC](#cell-solving))\n",
    "---\n",
    "***Multicollinearity*** (the degree to which the covariates are linear combinations of each other)<br> figures prominently in ***linear model regression*** contexts and <u>is driven by ***singular values***</u>\n",
    "\n",
    "For ***design matrix*** $X_{n\\times p} = U_{n\\times r} D_{r \\times r} (V^T)_{r\\times p}$\n",
    "\n",
    "- $r<p$ means some columns of $X$ are perfectly ***collinear*** making $X$ statistically intractable without alteration\n",
    "\n",
    "- $r=p$ means $X$ is technically ***full rank***; but, whenever ***singular values*** $\\lambda_j = D_{jj}$ are relatively very small<br>the numerical contribution of ***loadings*** $U_{\\cdot j}$ and ***basis vectors*** $V_{\\cdot j}$ constructing $X$ degrade due ***roundoff error*** \n",
    "    - (and if totally lost in ***roundoff error***, then $X$ IS ***non-full rank*** numerically speaking)\n",
    "\n",
    "When \n",
    "$$X_{n\\times p} = U_{n\\times p} D_{p \\times p} (V^T)_{p\\times p} \\approx U_{n\\times r} D_{r \\times r} (V^T)_{r\\times p} \\;\\text{ for } r<p$$\n",
    "\n",
    "then $X$ is behaving numerically like it's characteristically ***non-full rank***, which is exactly when there's ***high multicollinearity***\n",
    "- The relative magnitudes of the ***singular values*** of $X$ characterize the degree the ***multicollinearity*** present in $X$...\n"
   ]
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   "source": [
    "<a name=\"cell-sovling-Axb-math-multicollinearity\"></a>\n",
    "\n",
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "***Variance Inflation Factors (VIFs)*** $\\frac {1}{1-R_{j}^{2}}$ quantify  ***multicollinearity*** <font style=\"color:gray\">(which might also be called \"observed covariate confounding\")</font>\n",
    "\n",
    "> $R_{j}^{2}$ is the ***coefficient of determination*** for the regression of $X_{j}$ on all others except $X_{j}$\n",
    "> \n",
    "> $${\\displaystyle X_{j}= \\alpha_{0}+\\alpha_{1}X_{1} + \\alpha_{2}X_{2}+\\cdots + \\underset{\\text{no } X_j}{\\alpha_{j-1}X_{j-1} + \\alpha_{j+1}X_{j+1}}+\\cdots\\alpha_{k}X_{p}}+\\epsilon$$\n",
    "\n",
    "The more predictive $X_{j}$ is of the others the larger $R^2_j$ is and the more the coefficient uncertainty *inflates*\n",
    "\n",
    "$$ {\\displaystyle {\\widehat {\\operatorname {var} }}({\\hat {\\beta }}_{j})=s^{2}[(X^{T}X)^{-1}]_{jj} =  {\\frac {s^{2}}{(n-1){\\widehat {\\operatorname {var} }}(X_{j})}}\\cdot \\underset{VIF}{\\frac {1}{1-R_{j}^{2}}}} \\quad \\begin{array}{ll}\\text{$s^2$ is the }\\textbf{residual variance}\\\\\\text{ of the original regression}\\end{array}$$\n",
    "\n",
    "But this can be reformulated in terms of ***singular values*** which shows that\n",
    "\n",
    "- it's small ***singular values*** $\\lambda_i = D_{jj}$ of ***design matrix*** $X$ lead to *inflated* ${\\widehat {\\operatorname {var} }}({\\hat {\\beta }}_{j})$ \n",
    "$${\\widehat {\\operatorname {var} }}({\\hat {\\beta }}_{j})=s^{2}[(X^{T}X)^{-1}]_{jj} = s^{2}[(VD^2V^T)^{-1}]_{jj} = s^{2}[(VD^{-2}V^T)]_{jj} = s^2 \\sum_{i=1}^{p}V_{ji}^2D_{ii}^{-2}$$\n"
   ]
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   "source": [
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {
    "id": "LbvCD6r5qkec"
   },
   "outputs": [],
   "source": [
    "import numpy as np; from scipy import stats; import statsmodels.api as sm; import matplotlib.pyplot as plt\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor as VIF # https://en.wikipedia.org/wiki/Variance_inflation_factor#Calculation_and_analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {
    "id": "tbpRFzwXhMh6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X columns ARE standardized: column means [ 3.3306691e-18 -3.0531133e-17] column standard deviations [1. 1.]\n",
      "['Condition No.:' '1']\n"
     ]
    },
    {
     "data": {
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coef.</th>\n",
       "      <th>Std.Err.</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "      <th>[0.025</th>\n",
       "      <th>0.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.921432</td>\n",
       "      <td>0.093664</td>\n",
       "      <td>9.837616</td>\n",
       "      <td>3.006022e-16</td>\n",
       "      <td>0.735535</td>\n",
       "      <td>1.107329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1.004436</td>\n",
       "      <td>0.093924</td>\n",
       "      <td>10.694130</td>\n",
       "      <td>4.280968e-18</td>\n",
       "      <td>0.818023</td>\n",
       "      <td>1.190850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>0.899762</td>\n",
       "      <td>0.093924</td>\n",
       "      <td>9.579673</td>\n",
       "      <td>1.084414e-15</td>\n",
       "      <td>0.713349</td>\n",
       "      <td>1.086175</td>\n",
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       "          Coef.  Std.Err.          t         P>|t|    [0.025    0.975]\n",
       "const  0.921432  0.093664   9.837616  3.006022e-16  0.735535  1.107329\n",
       "x1     1.004436  0.093924  10.694130  4.280968e-18  0.818023  1.190850\n",
       "x2     0.899762  0.093924   9.579673  1.084414e-15  0.713349  1.086175"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# very low multicollinearity so there's minimal variance inflation\n",
    "n = 100; X = stats.multivariate_normal(cov=np.array(((1,.09),(.09,1)))).rvs(n); X=(X-X.mean(axis=0))/X.std(axis=0); print(\"X columns ARE standardized:\", \"column means\", X.mean(axis=0), \"column standard deviations\",  X.std(axis=0))\n",
    "X = sm.add_constant(X); Y = X.dot(np.ones(3)) + stats.norm().rvs(n); model = sm.OLS(Y,X); results = model.fit(); print(results.summary2().tables[2].values[3,2:]); results.summary2().tables[1]"
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   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance Inflation Factors 1.0 1.005558001090048 1.0055580010900482\n"
     ]
    }
   ],
   "source": [
    "print(\"Variance Inflation Factors\", VIF(X,0),VIF(X,1),VIF(X,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s(X^TX)^{-1/2}                   [0.0936643 0.0939242 0.0939242]\n",
      "s(VIF/(n-1)*Var[X])^{-1/2}       [0.0936643 0.0939242 0.0939242]\n",
      "\n",
      "Singular Values [10.365064795662562, 10.0, 9.621093065848424] Singular Values^{-2} [0.00930799105524602, 0.01, 0.010803168966554947]\n",
      "s*(SUM_i V_ij^2 D_ii^{-2})^{1/2} [0.0936643 0.0939242 0.0939242]\n"
     ]
    }
   ],
   "source": [
    "s = (float(results.summary2().tables[0].iloc[-1,-1]))**.5 # residual error\n",
    "XtXinv = np.linalg.inv(X.T.dot(X)); print('s(X^TX)^{-1/2}                  ', s*np.diag(XtXinv)**0.5)\n",
    "VIF_formula = np.array([VIF(X,0),VIF(X,1),VIF(X,2)]) # This formula doesn't work for the intercept since Var(X_intercept)=0\n",
    "VIF_formula[1:] = s*(VIF_formula[1:]/((n-1)*X.var(ddof=1,axis=0)[1:]))**0.5; VIF_formula[0] = s*XtXinv[0,0]**0.5; print('s(VIF/(n-1)*Var[X])^{-1/2}      ', VIF_formula)\n",
    "U,D,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "print(\"\\nSingular Values\", list(D), \"Singular Values^{-2}\", list(D**(-2)))\n",
    "XtXinv_by_svd = (Vt.T*D**(-2)).dot(Vt) # will be the same (sans numeric error) to XtXinv\n",
    "XtXinv_by_svd_diag = (Vt.T**2*D**-2).sum(axis=1); print('s*(SUM_i V_ij^2 D_ii^{-2})^{1/2}', s*XtXinv_by_svd_diag**0.5) \n",
    "# confirming that these coefficient variances depend on the singular values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {
    "id": "t9KQzbk3hfAt"
   },
   "outputs": [
    {
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vv/8+ZsyYgfHjx6NZs2bo1KkT/v33X3z++ef46KOP9OpJZuLEifDz80NYWBhiYmIwZswY9OnTB8WKFUPNmjWxceNGnD17FhMnToSNjQ2WLFmiXDcqKgp9+/ZVBv7nz5/HzJkzcfXqVaxevRqA/Iv2jz/+GFFRUdi6davO9hj6ORaQBzZ+fn4IDg7Wa+w9U1NTrFmzBvXq1UPdunURFRWFTZs2wdnZWee66owaNQpr167FjBkzULt2bSQkJODSpUt48uSJ1vXu3buHevXq4e3bt8rn1idPnmDPnj149uyZyvAg+pyHqKgoNGrUCIMHD4atrS1iYmKwcOFCvP/++7h48WKm141u3bqhd+/e+PTTT5U/4oiJiUGlSpXQu3dv2NvbIzY2FitWrEC9evVw+fJlODo66tX2OnXqIDQ0VPk9hOKHC4rq7L///hvt2rVDgwYN8P3338PW1habNm1Cr169kJiYmCmk0uc10FCvt+nt2bMH/v7+qFKlChYuXAh3d3fExMTgr7/+Ui5jyNeFTz75BDNnzsQPP/yAGTNmKKc/ffoUmzZtwrBhw1C8eHG16y5fvhwbN27EjBkzEBoaisqVKxu0IlJfOblfKQwePBgdOnTAhg0bcOfOHYwdOxYfffRRpu/qFIQQGDt2LJYsWYKVK1cW3bF0BRERUTbExcWJ999/XwAQAISpqalo3LixCAkJES9fvlRZtnnz5qJ58+bK29HR0QKA8PHxESkpKcrpJ0+eFADExo0bhRBCpKamCmdnZ9GgQQOV7d26dUuYmpqKcuXKKaf9/fffAoD4+++/VZZV7Cs0NFQ5LTg4WGh7CUxLSxNv374VERERAoA4f/68ct6AAQMEALF69Wpdp0jl+B0dHcWbN2+U00aPHi0AiOvXr6tdJyUlRbx9+1a0bNlSdO3aVWUeABEcHKzzeEJDQwUAER0dLYQQ4vbt26JYsWLiiy++UFnu5cuXwtnZWfTs2VMIIb+2AMSiRYv0PkYiIiIynA0bNggAwtnZOdP7Km0yvucaNmyYKFmyZJb3r3j/VKZMGZGUlKSc/uLFC2Fvby9atWqlnNawYUNRqlQplXampKSI6tWri7Jly4q0tDQhhBC9e/cW5ubm4vbt2yr7at++vbC0tBTPnz8XQrx7T9esWbNM7VL3fi84OFiYmZmJhw8fKqdt3rxZABARERFaj7NFixaiZMmS4tGjRxqXyWq7P/jgA5XlfvnlFwFAHD9+XAghxKlTpwQAsW3bNq1ts7KyEgMGDMg0XfH+LiAgINO8AQMGqLw/Vsj4XvHQoUMCgJg0aZLWNlSrVk3l/qQQEhIiZDKZiIyMVJn+22+/CQDizz//FEIIsWvXLgFALF68WGW5mTNnZno/q87KlSsFAOW5nzFjhqhcubLo1KmTGDhwoBBCiDdv3ggrKysxceJEjcer7Vj0vW76SklJEW/evBEVK1YUI0eO1Ll8uXLlVK7z+PHjBQBx4sQJleU+++wzIUmSuHbtmhBCiH379gkA4tChQ0IIIdatWydsbGzE0KFDhZ+fn3K9ihUrir59+ypvt23bVpQtW1bEx8erbH/YsGGiePHi4unTp0II7Y9DdRTPGV5eXiqfedRRfM4ZNGiQqF27tso8AKJ06dLixYsXymkPHjwQMplMhISEKKcprvHjx4/F2rVrhZmZmRg+fLhITU3Vq70Z26PuminOQZ06dZTPY0IIERMTI0xNTcXgwYOV0xSfETXd148cOaJyjLa2tspzraDvc2laWpr44IMPRMmSJcWlS5dE1apVReXKlcWrV69UtpfxvqU4Hn9/f5XlRowYIQCI4cOHq0zv0qWLsLe313jeUlNTxdu3b8XPP/8sTExMVI6nQ4cOap+LFMef/rFv6OdYIYQ4ePCgMDExEVOnTtXYfnU+/vhjAUB07NgxS+tlPKbq1auLLl26ZGkbQggRFBQkTE1NxeXLlzUuk93nLMV3HLdu3RIAxO+//66cp3g8TZ48WWcbU1JSxKtXr4SVlZXK/V2ftkdGRmb6bkahcuXKonbt2uLt27cq0zt27ChcXFyUj21tr4EZv//I6eutuvccXl5ewsvLS+W9kS6anmPUfVeV8RiEkD+/lCpVSiQnJyunzZkzR8hkMpXl1FFsL+PrdcbnBwVN393paqM6hrhfKfY1dOhQleXnzp0rAIjY2FiVY+rQoYNITEwU3bt3F7a2tmLfvn06912YsatPIiLKFgcHBxw+fBiRkZGYPXs2OnfujOvXr2PChAnw8fHJ1H2EOh06dFD5BW2NGjUAQFnef+3aNTx48AA9e/ZUWc/d3R1NmjQx4NHIu7bs27cvnJ2dYWJiAlNTUzRv3hwAcOXKlUzLd+/eXe9tDxo0CHFxccquk1JSUrBu3To0bdoUFStWVC73/fffo06dOihevDiKFSsGU1NT7N+/X+3+s2PPnj1ISUlBQEAAUlJSlH/FixdH8+bNlV1Y2Nvbw8vLC/PmzcPChQtx9uxZla6FiIiIKPcoumCUyWR49OgRzp8/n+1t1a9fH8+fP0efPn3w+++/6/X+LL1u3bqp/JLcxsYG/v7+OHToEFJTU5GQkIATJ06gR48esLa2Vi5nYmKC/v374+7du8quxw4cOICWLVvCzc1NZR+BgYFITEzM1F2nvu+1PvvsMwDyruEVli5dCh8fHzRr1kzjeomJiYiIiEDPnj21/gI+q+3u1KmTyu2M728rVKgAOzs7jBs3Dt9//73e1ZcZZeW9aEa7du0CAJVuNLNix44dqF69OmrVqqXynrJt27Yq3aL9/fffAIB+/fqprK+o1NOlVatWAKCs+tu7dy9at26NVq1aYe/evQDk1RoJCQnKZbNL13XTJCUlBbNmzULVqlVhZmaGYsWKwczMDDdu3MjWe/gDBw6gatWqmcZiCgwMhBBCWd3QpEkTFC9eXOXc+Pr6ol27djh27BgSExNx584d3LhxQ3luXr9+jf3796Nr166wtLRUuXYffPABXr9+nWnYhazezzp16qS28ubXX39FkyZNYG1trfycs2rVKrXnyM/PDzY2NsrbpUuXRqlSpdRei5kzZyIwMBCzZ8/G4sWLMw05oU5Wr1nfvn1VuqosV64cGjdurLx/p6fpvp5x2RYtWsDOzk55OyvPpZIk4eeff4aNjQ3q1q2L6Oho/PLLL7CystJ57ADQsWNHldtVqlQBgExdx1apUgVPnz5V6e7z7Nmz6NSpExwcHJSfmQMCApCamqpXF77qGPo5FgCaN2+OlJQUTJ48We923L9/H7/++itkMhlOnz6NZ8+eZfVQlOrXr49du3Zh/PjxOHjwIJKSkvRab9euXfDz81NeE230OQ+PHj3Cp59+Cjc3N+Xjrly5cgD0/47j1atXGDduHCpUqIBixYqhWLFisLa2RkJCgso2stL2jG7evImrV68qHz8Zn5tiY2MzdWOqz3OToV5vFa5fv46oqCgMGjRIY5Wdov2GfF348ssv8ejRI/z6668A5O8TV6xYgQ4dOqjt3ju/ycn9SkHf1+gnT56gRYsWOHnypLLr5KKMwR8REeVI3bp1MW7cOPz666+4f/8+Ro4ciZiYGMydO1fnug4ODiq3FV3uKN4YK7rCSN+lhYK6adn16tUrNG3aFCdOnMCMGTNw8OBBREZGIjw8XKU9CpaWllq7f8hI0bVQaGgoAODPP//Ew4cPVbpiWbhwIT777DM0aNAAW7ZswT///IPIyEi0a9dO7w8KuijGBahXrx5MTU1V/jZv3qz8MlCSJOzfvx9t27bF3LlzUadOHTg5OWH48OHKLjGIiIgod8yfPx/Hjx/Hhg0bULFiRQQFBWX7vUD//v2xevVq3Lp1C927d0epUqXQoEEDZWiii7puzpydnfHmzRu8evUKz549gxACLi4umZZTdLGpeD/35MkTvZZTULesOqVLl0avXr3www8/IDU1FRcuXMDhw4cxbNgwres9e/YMqampym7GNMlqu3W9v7W1tUVERARq1aqFiRMnolq1aihTpgyCg4NVxsnSRd/zo87jx49hYmKS7W7sHj58iAsXLmR6P2ljYwMhhPI95ZMnT1CsWLFM50Tf/ZYrVw5eXl7Yt2+fMgBQBH+KIGTfvn2wsLBA48aNs3UsCrqumyajRo3CN998gy5dumD79u04ceIEIiMjUbNmzWw9bvW9vxUvXhxNmjRRBn/79+9H69at4evri9TUVBw+fFj5OFcEf0+ePEFKSgq+++67TNfugw8+AIBMPw7I6v1M3fLh4eHo2bMnXF1dsW7dOhw/fhyRkZEICgpSOzZVxmsByK+HuvO5bt06uLq6onfv3nq3MavXTNPzYMbHvrb7uq7nt6w8lwLyc9SpUye8fv0a7dq1U3blqg97e3uV22ZmZlqnK67R7du30bRpU9y7dw+LFy9W/ghYMT5kdl+nDP0cm11DhgxBamoqdu3ahWfPnmH48OHZ3taSJUswbtw4bNu2DX5+frC3t0eXLl1w48YNres9fvxY52uSgq7zkJaWhjZt2iA8PBxfffUV9u/fj5MnTyrDfXXnS9116Nu3L5YuXYrBgwdjz549OHnyJCIjI+Hk5KSyjay0PSPF9xRjxozJ9Nw0dOhQANl7bjLU663C48ePAUDncRr6daF27dpo2rSp8rG2Y8cOxMTE6Hyfk1/k5H6loO/j/vr16zhx4gTat2+P6tWrG/AoCiaO8UdERAZjamqK4OBgfPvtt7h06VKOt6d4cc84kDWATGO8KH5xlXHsP31+2X7gwAHcv38fBw8eVFb5AdA4nl36X3zqw8LCAn369MFPP/2E2NhYrF69GjY2Nvjwww+Vy6xbtw6+vr5YsWKFyrr6BG3pjz39eCUZj13RT/pvv/2m/KWfJuXKlVMODn/9+nX88ssvmDJlCt68eYPvv/9eZ5uIiIgo6y5fvozJkycjICAAvXr1Qrly5dCkSRNMmjQJCxcuzNY2Bw4ciIEDByIhIQGHDh1CcHAwOnbsiOvXr+t8P5Dx/ZZimpmZmbJyRyaTITY2NtNy9+/fB/Du/YeDg4Neyylk5f3Wl19+ibVr1+L333/H7t27UbJkyUyVNxnZ29vDxMQEd+/e1bpcVtutDx8fH2zatAlCCFy4cAFhYWGYNm0aLCwsMH78eL22oe78FC9eXO042BnfEzo5OSE1NRUPHjzIVoDo6OgICwsL5Zhe6uYD8nOXkpKCJ0+eqHxpp+5+pUnLli3x+++/IyIiAmlpafD19YWNjQ3KlCmDvXv3Yt++fWjatGmmMfvyyrp16xAQEIBZs2apTI+Li9M45qA2Wbm/tWzZEpMnT8bJkydx9+5dtG7dGjY2NqhXrx727t2L+/fvw9vbW1lJZWdnp6wg01Tt6enpqXI7q5971C2/bt06eHp6YvPmzSrzDTFm++7du9GrVy80bdoU+/fv1/mcpmhPVq6ZpufBjF9Ea7uvZ1w243mys7PT+7kUkFd4rlixAvXr18fWrVuxZcuWHFUB62Pbtm1ISEhAeHi4ynk+d+5cjrabG8+xWbVq1Sr8+eefWL16Ndq0aYOpU6di3Lhx6NmzJ/z9/bO8PSsrK0ydOhVTp07Fw4cPldV//v7+uHr1qsb1nJycdL4m6evSpUs4f/48wsLCMGDAAOX0mzdvalwn4/0yPj4eO3bsQHBwsMprk2LcTkO1XXGNJ0yYgG7duqldJuO4ePo+Nxni9VZB0TuAruM09OsCAAwfPhwffvghzpw5g6VLl8Lb2zvb4z8D2t8vGPoxl5P7VVY1atQIH374ofJH9itWrNCrErywKrpHTkREOaLuzTnwrssIxS/0cqJSpUpwdnbGL7/8ojL99u3bOHbsmMo0RRcHFy5cUJmu6F5TG8UbkYxfGPzwww9ZbbJGgwYNQmpqKubNm4c///wTvXv3Vhl0XpKkTPu/cOFCpq5N1NF07BkHkW/bti2KFSuGqKgo1K1bV+2fOt7e3vj666/h4+ODM2fO6HO4RERElEUpKSkYMGAAHB0dsXjxYgBAw4YNMWrUKCxevBhHjx7N0fatrKzQvn17TJo0CW/evMG///6rc53w8HCVipyXL19i+/btaNq0KUxMTGBlZYUGDRogPDxc5VfXaWlpWLduHcqWLQtvb28A8pBC8WOr9H7++WdYWlqiYcOG2T629957D40bN8acOXOwfv16BAYG6uz2zsLCAs2bN8evv/6q9YdiudluSZJQs2ZNfPvttyhZsqTK+yxNFU7aeHh44NGjRyo/mnvz5g327Nmjslz79u0BINMPzjLS1IaOHTsiKioKDg4Oat9PKt6b+vn5AQDWr1+vsv6GDRv0PqZWrVrh4cOHWLRoERo2bKjsArJly5bYunUrIiMj9ermMzvnUx/q3sPv3LkT9+7dy9b2WrZsicuXL2d6z/3zzz9DkiTlOQXk5yYlJQXffPMNypYti8qVKyun79u3DwcOHFA5N5aWlvDz88PZs2dRo0YNtddOXbVdTkmSBDMzM5Uvfx88eIDff/89x9suV64cDh8+DHNzczRt2lRnRZWiPVm5Zhs3boQQQnn71q1bOHbsGHx9fTMtq+m+rm7Z9LLyXBobG4uPPvoIzZs3x7Fjx9CpUycMGjQI0dHRWveRU+o+MwshVLpZVsjK4y03n2P1cfv2bYwaNQodOnTAwIEDAQCjR49GgwYN8Mknn+Soy09AXpUeGBiIPn364Nq1a0hMTNS4bPv27fH3339n6tYyOwzxHYckSRBCZNrGypUrkZqaqjJNn7ZrqtKqVKkSKlasiPPnz2v8niJ997/ZYYjXW29vb3h5eWH16tVaf7hg6NcFAOjatSvc3d0xevRo7Nu3D0OHDs3yDzPS8/DwyPT90fXr1w1y39MlK/er7BgwYAA2bdqE0NBQZVfERRUr/oiIKFvatm2LsmXLwt/fH5UrV0ZaWhrOnTuHBQsWwNraGl9++WWO9yGTyTB16lR88skn6NGjB4KCgvD8+XNMnToVLi4uKr/ccXZ2RqtWrRASEgI7OzuUK1cO+/fvV3bXqU3jxo1hZ2eHTz/9FMHBwTA1NcX69etzNKZORnXr1kWNGjWwaNEiCCFUuvkE5F+gTJ8+HcHBwWjevDmuXbuGadOmwdPTEykpKVq3/cEHH8De3h6DBg3CtGnTUKxYMYSFheHOnTsqy3l4eGDatGmYNGkS/vvvP7Rr1w52dnZ4+PAhTp48qfxl4oULFzBs2DB8+OGHqFixIszMzHDgwAFcuHAhy7+KIyIiIv2EhITg1KlT2LVrl8ovwqdPn47t27cjKCgI586dg4WFhd7bHDJkCCwsLNCkSRO4uLjgwYMHCAkJga2tLerVq6dzfRMTE7Ru3RqjRo1CWloa5syZgxcvXmDq1Kkq7W7dujX8/PwwZswYmJmZYfny5bh06RI2btyo/GIqODgYO3bsgJ+fHyZPngx7e3usX78eO3fuxNy5c2Fra6v/yVLjyy+/RK9evSBJkrJrMF0WLlyI999/Hw0aNMD48eNRoUIFPHz4EH/88Qd++OEH2NjYGLzdO3bswPLly9GlSxeUL18eQgiEh4fj+fPnKr/e9/HxwcGDB7F9+3a4uLjAxsYmU8VDRr169cLkyZPRu3dvjB07Fq9fv8aSJUsyfenVtGlT9O/fHzNmzMDDhw/RsWNHmJub4+zZs7C0tMQXX3yhbMOmTZuwefNmlC9fHsWLF4ePjw9GjBiBLVu2oFmzZhg5ciRq1KiBtLQ03L59G3/99ZfyS/M2bdqgWbNm+Oqrr5CQkIC6devi6NGjWLt2rd7nq0WLFpAkCX/99ZfK/a5Vq1bKKhZ9gj9Nx5JTHTt2RFhYGCpXrowaNWrg9OnTmDdvXra7vBs5ciR+/vlndOjQAdOmTUO5cuWwc+dOLF++HJ999pky/AHkgbednR3++usvZWAByM/H9OnTlf9Pb/HixXj//ffRtGlTfPbZZ/Dw8MDLly9x8+ZNbN++XTmGoCF17NgR4eHhGDp0KHr06IE7d+5g+vTpcHFx0Suo08XFxQURERFo27YtmjVrhr1792rt4i2r1+zRo0fo2rUrhgwZgvj4eAQHB6N48eKYMGGCynJmZmZYsGABXr16hXr16uHYsWOYMWMG2rdvj/fff1/ncejzXJqamoo+ffpAkiRs2LABJiYmCAsLQ61atdCrVy8cOXJE2UWnobVu3RpmZmbo06cPvvrqK7x+/RorVqxQG4z5+PggPDwcK1aswHvvvQeZTKbxR6a58doQERGhrIjVNs6f4nO5iYmJSoCpOK+1a9fG8OHDs/ScBQANGjRAx44dUaNGDdjZ2eHKlStYu3YtGjVqpPLj34ymTZuGXbt2oVmzZpg4cSJ8fHzw/Plz7N69G6NGjVKG+/qoXLkyvLy8MH78eAghYG9vj+3bt+vd1TcAlChRAs2aNcO8efPg6OgIDw8PREREYNWqVZkq1/Rpu5eXFywsLLB+/XpUqVIF1tbWKFOmDMqUKYMffvgB7du3R9u2bREYGAhXV1c8ffoUV65cwZkzZ5Tj22VFbrzeLlu2DP7+/mjYsCFGjhwJd3d33L59G3v27FEG/4Z+XQDk98nPP/8c48aNg5WVFQIDA7O9LUDeFfxHH32EoUOHonv37rh16xbmzp2rdcxjQ8nK/Sq7evToAUtLS/To0QNJSUnYuHFjrj035muCiIgoGzZv3iz69u0rKlasKKytrYWpqalwd3cX/fv3F5cvX1ZZtnnz5qJ58+bK29HR0QKAmDdvXqbtAhDBwcEq03788UdRoUIFYWZmJry9vcXq1atF586dRe3atVWWi42NFT169BD29vbC1tZWfPTRR+LUqVMCgAgNDVUuFxwcLDK+BB47dkw0atRIWFpaCicnJzF48GBx5syZTOsOGDBAWFlZZe1k/d/ixYsFAFG1atVM85KTk8WYMWOEq6urKF68uKhTp47Ytm2bGDBggChXrpzOc3Ty5EnRuHFjYWVlJVxdXUVwcLBYuXKlACCio6NVlt22bZvw8/MTJUqUEObm5qJcuXKiR48eYt++fUIIIR4+fCgCAwNF5cqVhZWVlbC2thY1atQQ3377rUhJScnWsRMREZFm586dE6ampmLIkCFq5x8/flzIZDIxcuRIrdvJ+J5rzZo1ws/PT5QuXVqYmZmJMmXKiJ49e4oLFy5o3Y7ivdqcOXPE1KlTRdmyZYWZmZmoXbu22LNnT6blDx8+LFq0aCGsrKyEhYWFaNiwodi+fXum5S5evCj8/f2Fra2tMDMzEzVr1lR5nyWEEH///bcAIH799ddM6yvm/f3335nmJScnC3Nzc9GuXTutx5bR5cuXxYcffigcHByEmZmZcHd3F4GBgeL169cGabfiXCqWv3r1qujTp4/w8vISFhYWwtbWVtSvX1+EhYWprHfu3DnRpEkTYWlpKQAor2toaKgAICIjI9Uez59//ilq1aolLCwsRPny5cXSpUvVvvdNTU0V3377rahevbowMzMTtra2olGjRirXLSYmRrRp00bY2NgIACrvSV+9eiW+/vprUalSJeX6Pj4+YuTIkeLBgwfK5Z4/fy6CgoJEyZIlhaWlpWjdurW4evWq2vezmtSuXVsAEEePHlVOu3fvngAgHBwcRFpamsry6o5X07Hoe900efbsmRg0aJAoVaqUsLS0FO+//744fPhwpseiJuXKlRMDBgxQmXbr1i3Rt29f4eDgIExNTUWlSpXEvHnzRGpqaqb1u3btKgCI9evXK6e9efNGWFlZCZlMJp49e5ZpnejoaBEUFCRcXV2FqampcHJyEo0bNxYzZsxQLqPtcaiOts93Qggxe/Zs4eHhIczNzUWVKlXETz/9pPY6ARCff/55pvUznifFuo8fP1ZOe/78uWjSpImwt7fX+PgQQv9rpjgHa9euFcOHDxdOTk7C3NxcNG3aVJw6dUplm4rPiBcuXBC+vr7CwsJC2Nvbi88++0y8evVKr2MUQvdz6aRJk4RMJhP79+9XWe/YsWOiWLFi4ssvv9R4zjRdU03PKerO8fbt20XNmjVF8eLFhaurqxg7dqzYtWtXpuflp0+fih49eoiSJUsKSZJUrrO6x74hn2PTL6vrOWbZsmWZHj/pzZ07VwAQv//+u9btZNzX+PHjRd26dYWdnZ0wNzcX5cuXFyNHjhRxcXFatyOEEHfu3BFBQUHC2dlZmJqaKl+3Hz58qHJs+pyHy5cvi9atWwsbGxthZ2cnPvzwQ3H79u1M7VV3rRXu3r0runfvLuzs7ISNjY1o166duHTpktrnLl1tF0KIjRs3isqVKwtTU9NM7Th//rzo2bOnKFWqlDA1NRXOzs6iRYsW4vvvv1cuo+01UDFP8f1HTl9vNb3nOH78uGjfvr2wtbUV5ubmwsvLS+X9mb7PMequWcZjSC8mJkYAEJ9++mmmeZpoOl9paWli7ty5onz58qJ48eKibt264sCBAzluY3qGuF9par+6a1OuXDnRoUOHTMtZW1uLdu3aicTERK3tLYwkIdLVqxMRERUAz58/h7e3N7p06YIff/zR2M0hIiIiKlRiYmLg6emJefPmYcyYMcZujl62b9+OTp06YefOnfjggw+M3RwiKuAOHjwIPz8//Prrr+jRo4fWZQMDA/Hbb7/h1atXedQ6IipqvvvuOwwfPhyXLl1CtWrVjN0cKgDY1ScREeVrDx48wMyZM+Hn5wcHBwfcunUL3377LV6+fGmQ7kSJiIiIqOC6fPkybt26hdGjR6NWrVrK8euIiIiICrqzZ88iOjoa06ZNQ+fOnRn6kd4Y/BERUb5mbm6OmJgYDB06FE+fPlUO8P3999/zDQ8RERFRETd06FAcPXoUderUwZo1a5RjChIREREVdF27dsWDBw/QtGlTfP/998ZuDhUg7OqTiIiIiIiIiIiIiIiIqBCQGbsBRERERERERERERERERJRzDP6IiIiIiIiIiIiIiIiICgEGf0RERERERERERERERESFQDFjNyA70tLScP/+fdjY2HDgbiIiIiIiKvSEEHj58iXKlCkDmYy/3+RnQiIiIiIiKkqy8pmwQAZ/9+/fh5ubm7GbQURERERElKfu3LmDsmXLGrsZRsfPhEREREREVBTp85mwQAZ/NjY2AOQHWKJECSO3hoiIiIiIKHe9ePECbm5uys9CRR0/ExIRERERUVGSlc+EBTL4U3TlUqJECX7IIyIiIiKiIoPdWsrxMyERERERERVF+nwm5OAQRERERERERERERERERIUAgz8iIiIiIiIiIiIiIiKiQoDBHxEREREREREREREREVEhUCDH+CMiIiIiIiLSJTU1FW/fvjV2M4iIiPINU1NTmJiYGLsZRESUixj8ERERERERUaEihMCDBw/w/PlzYzeFiIgo3ylZsiScnZ0hSZKxm0JERLmAwR8REREREREVKorQr1SpUrC0tOQXm0RERJD/MCYxMRGPHj0CALi4uBi5RURElBsY/BEREREREVGhkZqaqgz9HBwcjN0cIiKifMXCwgIA8OjRI5QqVYrdfhIRFUIyYzeAiIiIiIiIyFAUY/pZWloauSVERET5k+I1kuPgEhEVTgz+iIiIiIiIqNBh955ERETq8TWSiKhwY/BHRERERERERERERGRksfFJOBYVh9j4JGM3hajoir8HRB+S/1tAMfgjIiIiIiKiPLNixQrUqFEDJUqUQIkSJdCoUSPs2rXL2M0iKnQOHjwISZLw/PlzYzelQFm1ahXatGmT5fXCwsIgSRIkScKIESMM37AMFNdXkiR06dLFoNuOiYlRbrtWrVo53p5iWyVLllROGzNmDIYPH56t7Xl4eGDRokU5bhcAHDhwAJUrV0ZaWlqOtzVlyhTlsRqqfdqou88lJyfD3d0dp0+fzvX9k+FtjryNJrMPoO9PJ9Bk9gFsjrxt7CYRFT1nfgYWVQfW+Mv/PfOzsVuULQz+iIiIiIiIKM+ULVsWs2fPxqlTp3Dq1Cm0aNECnTt3xr///mvsphndgwcP8MUXX6B8+fIwNzeHm5sb/P39sX//fmM3zSD0/bLew8ND+WW2hYUFKleujHnz5kEIkfuNNJCwsDCVkCO3+fr6ZgqbGjdujNjYWNja2uZZO9RJTU1F48aN0b17d5Xp8fHxcHNzw9dff22klmWWnJyMyZMn45tvvlFOCwwMVBusnTt3DpIkISYmRjmtRIkSiI2NxfTp03PUjvPnz6NPnz5wc3ODhYUFqlSpgsWLF6sso7i+PXv2VLsNX19ftdMUjy1zc3O4urrC398f4eHharexb98+rc8/T58+xRdffIFKlSrB0tIS7u7uGD58OOLj41WWi42NzfTY/+qrrxAaGoro6GiN2zeUKVOmaAwwv/rqK0yaNAkymQwLFiyAra0tEhMTMy33+vVrlCxZEgsXLgQgDzO3bduWablq1aohNjYWH3/8scb2HDx4EJ07d4aLiwusrKxQq1YtrF+/PsvH1atXL8TGxqJRo0bKaebm5hgzZgzGjRuX5e2RccXGJ2FC+EWk/f+lLk0AE8MvsfKPKC/F3wO2fwmI//8YRKQB20cUyMq/YsZuQGHjMX6nsZtAVKjFzO5g7CYQERERUQ74+/ur3J45cyZWrFiBf/75B9WqVTNSq4wvJiYGTZo0QcmSJTF37lzUqFEDb9++xZ49e/D555/j6tWrxm5inpo2bRqGDBmC169fY9++ffjss89QokQJfPLJJ8ZumkG9efMGZmZmubJtMzMzODs758q2s8LExARr1qxRhhv9+vUDAHzxxRewt7fH5MmTjdzCd7Zs2QJra2s0bdo0W+tLkmSQc3769Gk4OTlh3bp1cHNzw7Fjx/Dxxx/DxMQEw4YNA/Du+lpYWCA5ORkAsGPHDpQpUwZ16tRRbmvTpk2oU6cOvL29AQBDhgzBtGnT8PbtW9y7dw9bt25F7969ERgYiB9//FGlHQ4ODnBwcNDYzvv37+P+/fuYP38+qlatilu3buHTTz/F/fv38dtvvymXc3Z2zhRAlypVCm3atMH333+POXPm5OyEZdOxY8dw48YNfPjhhwCAgIAATJgwAVu2bEH//v1Vlt2yZQsSExMzTc+oWLFiOu8Dx44dQ40aNTBu3DiULl0aO3fuREBAAEqUKJHpNVIbCwsLWFhYZHoO6devH8aOHYsrV66gSpUqem+PjCs6LkEZ+imkCoGYuES42FoYp1FERc3TqHehn4JIBZ7+B9i6GqdN2cSKPyIiIiIiIjKK1NRUbNq0CQkJCSoVC/lFXo6zM3ToUEiShJMnT6JHjx7w9vZGtWrVMGrUKPzzzz/K5W7fvo3OnTvD2toaJUqUQM+ePfHw4UPlfEVly+rVq+Hu7g5ra2t89tlnSE1Nxdy5c+Hs7IxSpUph5syZKvuXJAkrVqxA+/btYWFhAU9PT/z6668qy4wbNw7e3t6wtLRE+fLl8c033+Dt27cqy/zxxx+oW7cuihcvDkdHR3Tr1g2AvNLo1q1bGDlypLLiSBsbGxs4OzvDw8MDgwcPRo0aNfDXX38p57958wZfffUVXF1dYWVlhQYNGuDgwYMq2zh69CiaN28OS0tL2NnZoW3btnj27BkAeWXX8OHDUapUKRQvXhzvv/8+IiMjlesqulHcv38/6tatC0tLSzRu3BjXrl1TLnP+/Hn4+fnBxsYGJUqUwHvvvYdTp07h4MGDGDhwIOLj45XHOmXKFADyasYZM2YgMDAQtra2GDJkiNouOdVVk2k6nsDAQERERGDx4sXK/cXExKjd7pYtW1CtWjWYm5vDw8MDCxYsUDlnHh4emDVrFoKCgmBjYwN3d/dMYVB2VKxYESEhIfjiiy9w//59/P7779i0aRPWrFmTa8FndmzatAmdOnUydjMQFBSEJUuWoHnz5ihfvjw++ugjDBw4UGNlnkL58uUxYcIEBAcH4/nz5+jZsyciIiLg5OSkXMbS0hLOzs5wc3NDw4YNMWfOHPzwww/46aefsG/fviy1s3r16tiyZQv8/f3h5eWFFi1aYObMmdi+fTtSUlJ0rt+pUyds3LhR6zKPHj2Cv7+/8nlJXWWctufFsLAwTJ06FefPn1c+PsLCwgDIr3ebNm1QvHhxAICTkxP8/f2xevXqTPtYvXo1OnXqBCcnJ3h4eAAAunbtCkmSlLf1NXHiREyfPh2NGzeGl5cXhg8fjnbt2mHr1q1Z2o4mDg4OaNy4sc5zS/mLp6MVZBleGk0kCR6OlsZpEFFRZO8FSBkiM8kEsC9vnPbkAIM/IiIiIiIiylMXL16EtbU1zM3N8emnn2Lr1q2oWrWqxuWTk5Px4sULlb/clpfj7Dx9+hS7d+/G559/Disrq0zzFV1GCiHQpUsXPH36FBEREdi7dy+ioqLQq1cvleWjoqKwa9cu7N69Gxs3bsTq1avRoUMH3L17FxEREZgzZw6+/vprlUARAL755ht0794d58+fx0cffYQ+ffrgypUryvk2NjYICwvD5cuXsXjxYvz000/49ttvlfN37tyJbt26oUOHDjh79qwyNAOA8PBwlC1bFtOmTUNsbCxiY2P1OjdCCBw8eBBXrlyBqampcvrAgQNx9OhRbNq0CRcuXMCHH36Idu3a4caNGwDkwVnLli1RrVo1HD9+HEeOHIG/vz9SU1MByLv327JlC9asWYMzZ86gQoUKaNu2LZ4+faqy/0mTJmHBggU4deoUihUrhqCgIOW8fv36oWzZsoiMjMTp06cxfvx4mJqaonHjxli0aJGy28fY2FiMGTNGud68efNQvXp1nD59WqVLSW20Hc/ixYvRqFEjDBkyRLk/Nze3TNs4ffo0evbsid69e+PixYuYMmUKvvnmG2UIorBgwQLUrVsXZ8+exdChQ/HZZ5+pVJz6+voiMDBQr3an98UXX6BmzZoICAjAxx9/jMmTJ2d5/Dhd47BZW1tr/Wvfvr3W9Q8fPqy8zxrKlClTdAZD+iwTHx8Pe3t7rctUrVoVe/bswY0bN3D+/Hm0bt0aK1asgJ2dndb1BgwYADs7O53BoiJMTh9Iq2tniRIlUKyY7k7G6tevjzt37uDWrVsalwkMDERMTAwOHDiA3377DcuXL8ejR4+U83U9L/bq1QujR49WdsEZGxurnHfo0KFM13vQoEGIiIhQ6YI0JiYGf//9NwYNGgQAyh8JhIaGIjY2VuVHA5qOQV3Xq+npc32z8tirX78+Dh8+rNeylD+42FogpJsPTP7/wxgTScKsbtVZ7UeUl2xdAf/F8rAPkP/rv6jAVfsB7OqTiIiIiIiI8lilSpVw7tw5PH/+HFu2bMGAAQMQERGhMfwLCQnB1KlT86x9msbZaebtlCtfwN28eRNCCFSuXFnrcvv27cOFCxcQHR2tDHbWrl2LatWqITIyEvXq1ZO3Ny0Nq1evho2NDapWrQo/Pz9cu3YNf/75J2QyGSpVqoQ5c+bg4MGDaNiwoXL7H374IQYPHgwAmD59Ovbu3YvvvvsOy5cvBwCVsdg8PDwwevRobN68GV999RUAebetvXv3VrlWNWvWBADY29vDxMREWcmny7hx4/D111/jzZs3ePv2LYoXL47hw4cDkAebGzduxN27d1GmTBkAwJgxY7B7926EhoZi1qxZmDt3LurWratsOwBlV7IJCQlYsWIFwsLClEHQTz/9hL1792LVqlUYO3ascp2ZM2eiefPmAIDx48ejQ4cOeP36NYoXL47bt29j7NixyutWsWJF5Xq2trYau31s0aKFShB49+5dnedD2/EA8m4fFZVcmixcuBAtW7ZUho3e3t64fPky5s2bpxImfPDBBxg6dCgA+XX49ttvcfDgQeVxuru7w8XFRWebM1JUlVapUgU+Pj4YP358pmUOHDiAOXPm4Pz58yhXrhx69+6N3r17o3Tp0ti1axf27NmDJUuWaNzHuXPntLbBwkLz4/f58+d4/vy58j5lKI6OjvDy8srRMsePH8cvv/yCnTu1Dy9z7do1jBgxAvXq1UPNmjWxd+9enD17FjNnztQa/slkMnh7e2sN9AB5tWClSpVUQvj0njx5gunTp+vdJa+rq/yL1JiYGJQrVy7T/OvXr2PXrl34559/0KBBAwDAqlWrVLqv1Od50draWm0XnDExMZmud9u2bVGmTBllpSAgD/jKlCmDNm3aAICygrJkyZJ6PZ+5uLhoDa1/++03REZG4ocfftC6naw89lxdXXVeT8p/etVzRzNvJ8TEJcLD0ZKhH5Ex1AkAvFrKu/e0L18gQz+AwR8RERERERHlMTMzM1SoUAEAULduXURGRmLx4sUav/ScMGECRo0apbz94sULtRVNhpLX4+wIId+Zru4vr1y5Ajc3N5Vjr1q1KkqWLIkrV64ogz8PDw/Y2NgolyldujRMTEwgk8lUpqWvmgGQqbvVRo0aqQQpv/32GxYtWoSbN2/i1atXSElJQYkSJZTzz507hyFDhuh51NqNHTsWgYGBePz4MSZNmoQWLVqgcePGAIAzZ85ACKEcs0whOTlZOR7ZuXPnlON2ZRQVFYW3b9+iSZMmymmmpqaoX7++SoUjANSoUUP5f8UX7o8ePYK7uztGjRqFwYMHY+3atWjVqhU+/PBDnQEPgGxVlGk7Hn1duXIFnTt3VpnWpEkTLFq0CKmpqTAxkf+6Pf0xK8LL9PeVn3/+OdttWL16NSwtLREdHY27d+9mqnIbMmQIpk+fDh8fH0RGRmLt2rUYM2YMZDIZqlatiqVLl2rdvuJ5JTuSkuRd+iq6fTSUYcOGKcfly84y//77Lzp37ozJkyejdevWWrdz/fp1zJw5E3Xq1MGhQ4fwyy+/YOPGjXj8+LHOqj8hhM7noPr162scb/TFixfo0KEDqlatiuDgYK3bUVAEsYmJiWrnX7lyBcWKFVN5zFSuXFlZBa1YRp/nRXWSkpIyXW8TExMMGDAAYWFhCA4OhiRJWLNmDQIDA5WPkawKCQnROO/gwYMIDAzETz/9pHOc26w89iwsLDSeV8rfXGwtGPgRGZuta4EN/BQY/BEREREREZFRCSGQnJyscb65uTnMzc3zrD2KcXbSh3+5Oc5OxYoVIUkSrly5gi5dumhcTtMX8xmnZ6zGkSRJ7TRd3SYqlgOAf/75R1nN17ZtW9ja2mLTpk0qY8Rpq6bKKkdHR1SoUAEVKlTAli1bUKFCBTRs2BCtWrVCWloaTExMcPr06UxfxFtbW+tsi6agVd35TX/eFPMU523KlCno27cvdu7ciV27diE4OBibNm1C165dtR5bxu5cFYGsol0AMo2daIhzq+740u9TIbv3FV2OHz+Ob7/9Frt27cLcuXMxaNAg7Nu3T6VNp0+fVoY6Pj4+CAoKwosXL5CamqozuALeXX9NmjZtil27dqmd5+DgAEmSlONAKpQoUUJtV5SKsRNtbW11tiu7Ll++jBYtWmDIkCEqFbea+Pv7Z5rWp08fneulpqbixo0bWkMybV6+fIl27drB2toaW7du1VgRmJGia930YxCmp8+PIvR9XlTH0dEx0/UG5GMshoSE4MCBAwDkYwgOHDhQ67ayIyIiAv7+/li4cCECAgIMuu2nT59qPK9ERFT4cYw/IiIiIiIiyjMTJ07E4cOHERMTg4sXL2LSpEk4ePAg+vXrZ+ymKeX1ODv29vZo27Ytli1bhoSEhEzzFQFD1apVcfv2bdy5c0c57/Lly4iPj1fp+i67Mo75988//yi7dzx69CjKlSuHSZMmoW7duqhYsWKmMKRGjRrYv3+/xu2bmZkpx9jLCjs7O3zxxRcYM2YMhBCoXbs2UlNT8ejRI2U4qPhTdLunrS0VKlSAmZkZjhw5opz29u1bnDp1Ksvn0dvbGyNHjsRff/2Fbt26ITQ0NMvHqvhyPv24hxm7rDTEua1atarKMQPAsWPH4O3tne1KJn0lJSVhwIAB+OSTT9CqVSusXLlSbdeG6Su5FEqUKKFX6AfIz5u2v5UrV2pc18zMDFWrVsXly5dVpleuXBmXLl3C69evVaZHRkbCyclJ77Zl1b///gs/Pz8MGDAAM2fOzPL6Bw8e1HvZNWvW4NmzZ+jevXuW9/PixQu0adMGZmZm+OOPP7JUMXnp0iWYmppqrHSrUqUKUlJScOrUKeW0a9euKZ8TAf2eFzU9PmrXrp3pegOAl5cXmjdvjtDQUKxevRq+vr6ZqnlNTU2z9XymcPDgQXTo0AGzZ8/Gxx9/nO3taHLp0iXUrl3b4NslIqKCgcEfERERERER5ZmHDx+if//+qFSpElq2bIkTJ05g9+7dOruwy2u96rnjyHg/bBzSEEfG+6FXPfdc3d/y5cuRmpqK+vXrY8uWLbhx4wauXLmCJUuWKLvgbNWqFWrUqIF+/frhzJkzOHnyJAICAtC8efNsdR+Z0a+//orVq1fj+vXrCA4OxsmTJ5XdD1aoUAG3b9/Gpk2bEBUVhSVLlmDr1q0q6wcHB2Pjxo0IDg7GlStXcPHiRcydO1c538PDA4cOHcK9e/cQFxeXpbZ9/vnnuHbtGrZs2QJvb2/069cPAQEBCA8PR3R0NCIjIzFnzhz8+eefAOTdw0ZGRmLo0KG4cOECrl69ihUrViAuLg5WVlb47LPPMHbsWOzevRuXL1/GkCFDkJiYiEGDBunVnqSkJAwbNgwHDx7ErVu3cPToUURGRiqDBg8PD7x69Qr79+9HXFyc1i73KlSoADc3N0yZMgXXr1/Hzp07VSopdR2PYn8nTpxATEwM4uLi1FbojR49Gvv378f06dNx/fp1rFmzBkuXLlUZb1AfAQEBmDBhQpbWGT9+PNLS0jBnzhwA8rHKFixYgLFjxxp0HLKMQXDGP8WYcpq0bds2Uzjar18/FCtWDP3798epU6cQFRWFdevWISQkRGU8SE2WLl2Kli1bZmkZRejXunVrjBo1Cg8ePMCDBw/w+PFjnfvTJTExEQ8ePMDdu3dx4sQJjBs3Dp9++ik+++wz+Pn5aV335MmTqFy5Mu7duwdAXunXpk0bJCQkYNWqVXjx4oWyrfqEYocPH0bTpk1VKlorV66sfG6pVKkS2rVrhyFDhuDEiRM4ffo0Bg8erLK8Ps+LHh4eiI6Oxrlz5xAXF6esMFd3vRUGDRqE8PBwbN26Ve3zgoeHB/bv348HDx6orRpMb8KECSoVfYrQb/jw4ejevbvynCkqIDXJymPv8OHDyjEJiYio6GHwR0RERERERHlm1apViImJQXJyMh49eoR9+/blu9BPwcXWAo28HPJkrB1PT0+cOXMGfn5+GD16NKpXr47WrVtj//79WLFiBQB5d3fbtm2DnZ0dmjVrhlatWqF8+fLYvHmzQdowdepUbNq0CTVq1MCaNWuwfv16VK1aFQDQuXNnjBw5EsOGDUOtWrVw7NgxfPPNNyrr+/r64tdff8Uff/yBWrVqoUWLFjhx4oRy/rRp0xATEwMvL68sd0Hn5OSE/v37Y8qUKUhLS0NoaCgCAgIwevRoVKpUCZ06dcKJEyeU43x5e3vjr7/+wvnz51G/fn00atQIv//+O4oVk494Mnv2bHTv3h39+/dHnTp1cPPmTezZs0fv6i0TExM8efIEAQEB8Pb2Rs+ePdG+fXtMnToVANC4cWN8+umn6NWrF5ycnFQC0IxMTU2xceNGXL16FTVr1sScOXMwY8YMlWV0Hc+YMWNgYmKCqlWrwsnJCbdv3860nzp16uCXX37Bpk2bUL16dUyePBnTpk1DYGCgXsescPv2bZXqRF0iIiKwbNkyhIWFqXRzOmTIEDRu3BiDBg1S2+WoMQwZMgR//vkn4uPjldNsbW1x+PBhCCHQpUsX1KxZE3PnzsX06dMxevRonduMi4tDVFSUyjQPDw9MmTJF4zK//vorHj9+jPXr18PFxUX5l92uONP76aef4OLiAi8vL3Tt2hWXL1/G5s2bsXz5cp3rJiYm4tq1a8quaE+fPo0TJ07g4sWLqFChgkpb01fgabJx48ZM44Jeu3ZN5fyHhobCzc0NzZs3R7du3fDxxx+jVKlSyvn6PC92794d7dq1g5+fH5ycnLBx40YAwEcffYTLly/j2rVrmdrWvXt3ZTfT3bp1yzR/wYIF2Lt3L9zc3HRW1sXGxqo8JsPCwpCYmIiQkBCVc5Z+PzExMZAkSaVyU9/H3vHjxxEfH48ePXroXJaIiAonSeSXd1dZ8OLFC9ja2iI+Pl5lIPH8wGP8TmM3gahQi5ndwdhNICIiIspz+fkzkDFoOx+vX79GdHQ0PD09s9TlXFEnSRK2bt2qdYxBoqKgZ8+eqF27dparGsPCwjBixAiVbijVSUpKgr29Pf7880+dFXb6CAwMxPPnz7Ft27Ycb0shJiYGnp6eOHv2LGrVqmWQbWY8Pzt37sTYsWNx4cIFZYBtDF999RXi4+MzdTubHVOmTMG2bdsyddWbHQcPHkTXrl3x33//6fxBgq+vL2rVqoVFixYBAD788EPUrl0bEydO1LgOXyuJiAqerHwmZMUfERERERERERERgHnz5sHa2jpb68bHx8Pa2hrjxo3TuExERARatGiR49Dv8OHDsLa2xvr163O0HW0aN26Mxo0b53g71tbW+PTTT1WmJSQkIDQ01KihHwBMmjQJ5cqVy9F4feldvHgR1tbWelVQarN7925MnDhRa+i3fv16WFtb4/Dhw8ppycnJqFmzJkaOHJmj/RMRUcHGij8DY8UfUe5ixR8REREVRfn5M5AxsOLP8FjxR5QzL1++xMOHDwEAJUuWhKOjY67uLykpSTnWnrW1NZydnQ227ZSUFOXYi+bm5soudLPr5s2bAORd5Hp6eua0efnW06dPleP0OTk5wdbWNlf3l5P7HF8riYgKnqx8JjTuz2qIiIiIiIiIyOgK4G+CifIVGxsb2NjY5Nn+LCwsUKFChVzZdrFixQy67dxqZ35jb28Pe3v7PNtfXt/niIio4GBXn0RERERERERERERERESFAIM/IiIiIiIiIiIiIiIiokKAwR8RERERERERERERERFRIcDgj4iIiIiIiIiIiIiIiKgQYPBHREREREREREREREREVAgw+CMiIiIiIiIiIiIiIiIqBBj8ERERERERERVwvr6+GDFihPK2h4cHFi1aZLT2FGZTpkxBrVq1jN0MykVv3rxBhQoVcPToUaPs/9GjR3BycsK9e/eyvG5YWBhKlixpsLY0a9YMGzZsyPF2kpOT4e7ujtOnTxugVURERKQNgz8iIiIiIiIiIwsMDIQkSZn+bt68aeym5SuBgYHo0qVLnu1PkiRs27ZNZdqYMWOwf//+PGtDYfHnn3/CzMwMZ86cUZk+f/58ODo64sGDB0ZqWWY//vgjypUrhyZNmgAAYmJiIEkSzp07l2nZLl26IDAwMNN0X19ftdMUj21zc3O4urrC398f4eHhKsuVKlUK/fv3R3BwsCEORyd193MA2LFjBx48eIDevXvjzZs3cHR0xIwZM9RuIyQkBI6Ojnjz5o3acNzc3BxjxozBuHHjcuEIiIiIKD0Gf0RERERERET5QLt27RAbG6vy5+npmSf7fvPmTZ7sJ6+8ffs217ZtbW0NBweHXNt+YfXBBx8gICAAAQEBSE5OBgBcuXIF33zzDZYtWwZnZ2cjt/Cd7777DoMHD87yejt27MgUbG7atAnXr19X3h4yZAhiY2Nx8+ZNbNmyBVWrVkXv3r3x8ccfq6w3cOBArF+/Hs+ePcveQRjAkiVLMHDgQMhkMpiZmeGjjz5CWFgYhBCZlg0NDUX//v1hZmamcXv9+vXD4cOHceXKldxsNhERUZHH4I+IiIiIiIhInfh7QPQh+b95wNzcHM7Ozip/JiYmaqvcRowYobaiSF+KbYaEhKBMmTLw9vYGANy7dw+9evWCnZ0dHBwc0LlzZ8TExKisu3r1alSrVg3m5uZwcXHBsGHDlPNu376Nzp07w9raGiVKlEDPnj3x8OFD5XxFJdDatWvh4eEBW1tb9O7dGy9fvlQu89tvv8HHxwcWFhZwcHBAq1atkJCQgClTpmDNmjX4/ffflVVTBw8eVFZj/fLLL/D19UXx4sWxbt06tVVHixYtgoeHh17Ho1iua9eukCRJeTvjdtPS0jBt2jSULVsW5ubmqFWrFnbv3q2cr2hfeHg4/Pz8YGlpiZo1a+L48eNZuWSFwrfffotXr14hODgYKSkpCAgIgL+/P3r16mXspimdOXMGN2/eRIcOHbK8bvny5TFhwgQEBwfj+fPn6NmzJyIiIuDk5KRcxtLSEs7OznBzc0PDhg0xZ84c/PDDD/jpp5+wb98+5XI+Pj5wdnbG1q1bte4zLCwM7u7usLS0RNeuXfHkyZNMy6xYsQJeXl4wMzNDpUqVsHbtWuU8TffzuLg47Nu3D506dVIuO2jQIERFReHQoUMq2z98+DBu3LiBQYMGISwsDFOnTsX58+eVj9OwsDAAgIODAxo3boyNGzfqdT6JiIgoexj8EREREREREWV05mdgUXVgjb/83zM/G7tFBrd//35cuXIFe/fuxY4dO5CYmAg/Pz9YW1vj0KFDOHLkCKytrdGuXTtlReCKFSvw+eef4+OPP8bFixfxxx9/oEKFCgAAIQS6dOmCp0+fIiIiAnv37kVUVFSmUCcqKgrbtm3Djh07sGPHDkRERGD27NkAgNjYWPTp0wdBQUG4cuUKDh48iG7dukEIgTFjxqBnz54qlZGNGzdWbnfcuHEYPnw4rly5grZt2+p1DrQdT2RkJAB5JVNsbKzydkaLFy/GggULMH/+fFy4cAFt27ZFp06dcOPGDZXlJk2ahDFjxuDcuXPw9vZGnz59kJKSopyfPiAprGxsbLB69WosWLAA/fr1w507d7B8+fIsbyctLU3jvFmzZsHa2lrr3+HDhzWuf+jQIXh7e6NEiRJZblfVqlWxZ88e3LhxA+fPn0fr1q2xYsUK2NnZaV1vwIABsLOzy9TlZ/369bW29cSJEwgKCsLQoUNx7tw5+Pn5ZeqKc+vWrfjyyy8xevRoXLp0CZ988gkGDhyIv//+G4Dm+/mRI0dgaWmJKlWqKLfl4+ODevXqITQ0VGUfq1evRv369VG9enX06tULo0ePRrVq1ZSP0/TPAbqOiYiIiHKumLEbQERERERERJSvxN8Dtn8JiP+HCyIN2D4C8GoJ2Lrm2m537NgBa2tr5e327dvj119/zbX9WVlZYeXKlcqu+VavXg2ZTIaVK1dCkiQA8jCgZMmSOHjwINq0aYMZM2Zg9OjR+PLLL5XbqVevHgBg3759uHDhAqKjo+Hm5gYAWLt2LapVq4bIyEjlcmlpaQgLC4ONjQ0AoH///ti/fz9mzpyJ2NhYpKSkoFu3bihXrhwAedigYGFhgeTkZLXdQo4YMQLdunXL0jnQdjyKKq2SJUtq7YZy/vz5GDduHHr37g0AmDNnDv7++28sWrQIy5YtUy43ZswYZRXZ1KlTUa1aNdy8eROVK1cGAFSqVAm2trZZan9B1KJFC/To0QObNm3C5s2b4ejoqDL/1atXmD59OrZv344XL16gVatWGDBgAJo2bYonT55g8uTJGDp0KGrWrKl2+59++il69uyptQ2urpofxzExMShTpkzWDwzAtWvXMGLECNSrVw81a9bE3r17cfbsWcycOVNr+CeTyeDt7Z2putbV1RVnz57VuN7ixYvRtm1bjB8/HgDg7e2NY8eOqVSczp8/H4GBgRg6dCgAYNSoUfjnn38wf/58+Pn5abyfx8TEoHTp0pDJVGsGgoKCMGbMGCxduhTW1tZ49eoVfv31VyxcuBCA/DFqbW2NYsWKqX3cuLq6ZjpOIiIiMixW/BERERERERGl9zTqXeinIFKBp//l6m79/Pxw7tw55d+SJUtydX8+Pj4q43GdPn0aN2/ehI2NjbIyyt7eHq9fv0ZUVBQePXqE+/fvo2XLlmq3d+XKFbi5uSlDP0BeAVWyZEmVMb08PDyUoR8AuLi44NGjRwCAmjVromXLlvDx8cGHH36In376Se8xzurWrZul49d1PPp48eIF7t+/jyZNmqhMb9KkSaZxzGrUqKH8v4uLi7INClevXkXXrl2z3ZaC4v79+9i9ezcsLS3VVn59++23eP78OdasWYMNGzagZMmS6N27N4oXLw4vLy9YWFigUqVKGrdvb2+PChUqaP2zsLDQuH5SUhKKFy+erWO7fv06Zs6ciWnTpqFkyZL45Zdf0LRpUzx+/FjnukIIZeCuYGFhgcTERI3rXLlyBY0aNVKZlvH2lStX9Lp/ZqTpPPTp0wdpaWnYvHkzAGDz5s0QQiiDb110HRMRERHlHCv+iIiIiIiIiNKz9wIkmWr4J5kA9uVzdbdWVlbKbibTk8lkEEKoTHv79q1B9pdeWloa3nvvPaxfvz7Tsk5OTpkqfzJSF1yom25qaqoyX5IkZdeNJiYm2Lt3L44dO4a//voL3333HSZNmoQTJ07A09MzS8ej67xpC3+yKuNxqzsX6Y9bMU9bl5WF1eDBg1GzZk1MnToVLVu2RI8ePdC8eXPl/C+++AIlS5ZU3m7WrBkWLlyIBw8eoHTp0jAxMdG6/VmzZmHWrFlal9m1axeaNm2qdp6joyMuXryoMk1RiRkfH59p+efPnyurU/39/TPN79Onj9a2AEBqaipu3LihrDZVePr0qcr4gBllvH9ros/9MyNHR0e1obutrS169OiB0NBQDBo0CKGhoejRo4feXaPqOiYiIiLKOVb8EREREREREaVn6wr4L5aHfYD8X/9FudrNpzZOTk6IjY1VmXbu3DmD76dOnTq4ceMGSpUqlalCytbWFjY2NvDw8MD+/fvVrl+1alXcvn0bd+7cUU67fPky4uPjVcYJ00WSJDRp0gRTp07F2bNnYWZmhq1btwIAzMzMkJqaqtd2nJyc8ODBA5VwJP1503U8gDys07a/EiVKoEyZMjhy5IjK9GPHjmXpmIuKlStX4vDhwwgNDUXz5s0xbNgwBAUFISEhQblM+tBPQSaToUyZMjpDP0De1Wf6yll1f9qqQ2vXro2rV6+q3G/s7Ozg5OSUaZzHpKQk/Pvvv2orEA8ePKizrQpr1qzBs2fP0L17d5Xply5dQu3atTWuV7VqVfzzzz8q0zLerlKlis77p7r7ee3atfHgwQO14d+gQYNw9OhR7NixA0ePHsWgQYNU5mt7nOo6JiIiIso5Bn9EREREREREGdUJAEZcBAbskP9bJ8BoTWnRogVOnTqFn3/+GTdu3EBwcDAuXbpk8P3069cPjo6O6Ny5Mw4fPozo6GhERETgyy+/xN27dwEAU6ZMwYIFC7BkyRLcuHEDZ86cwXfffQcAaNWqFWrUqIF+/frhzJkzOHnyJAICAtC8eXO9u+E8ceIEZs2ahVOnTuH27dsIDw/H48ePlSGFh4cHLly4gGvXriEuLk5r5aOvry8eP36MuXPnIioqCsuWLcOuXbtUltF2PIr97d+/X2MAAgBjx47FnDlzsHnzZly7dg3jx4/HuXPnVMYN1EflypWVAWdhdPv2bYwePRrz589XVm/OmjULMplMOUadIeS0q08/Pz8kJCTg33//VZk+ZswYzJo1C2vXrkVUVBROnTqFgIAAFCtWDB999JHe7UtMTMSDBw9w9+5dnDhxAuPGjcOnn36Kzz77DH5+firLnT59Gm3atFFOW7p0qUrXtMOHD8fu3bsxd+5cXL9+HUuXLlUZ3w+Q3z/DwsLw/fff48aNG1i4cCHCw8MxZswY5TLq7ue1a9eGk5MTjh49mukYmjdvjgoVKiAgIAAVKlRAs2bNVOZ7eHggOjoa586dQ1xcHJKTk5XzDh8+rHJMREREZHgM/oiIiIiIiIjUsXUFPJsardJPoW3btvjmm2/w1VdfoV69enj58iUCAgwfRFpaWuLQoUNwd3dHt27dUKVKFQQFBSEpKUnZjd+AAQOwaNEiLF++HNWqVUPHjh1x48YNAPJKvW3btsHOzg7NmjVDq1atUL58eeVYYPooUaIEDh06hA8++ADe3t74+uuvsWDBArRv3x4AMGTIEFSqVAl169bVGEooVKlSBcuXL8eyZctQs2ZNnDx5UiXs0HU8ALBgwQLs3bsXbm5uGquUhg8fjtGjR2P06NHw8fHB7t278ccff6BixYp6HzcAXLt2TW1XkoWBEAJBQUFo2LAhPvnkE+V0S0tLhIaGYsWKFYiIiDBiC99xcHBAt27dMnV5O2bMGMyYMQPz589HzZo10aVLFwghcPjwYb27uQSAn376CS4uLvDy8kLXrl1x+fJlbN68GcuXL1dZ7vfff4e7u7tKl6RxcXGIiopS3m7YsCFWrlyJ7777DrVq1cJff/2Fr7/+WmU7Xbp0weLFizFv3jxUq1YNP/zwA0JDQ+Hr66tcRt393MTEBEFBQWq7/gWAoKAgPHv2DEFBQZnmde/eHe3atYOfnx+cnJywceNGAMDx48cRHx+PHj166H2+iIiIKOskoW+H4PnIixcvYGtri/j4+Cy9ucoLHuN3GrsJRIVazOwOxm4CERERUZ7Lz5+BjEHb+Xj9+jWio6Ph6emJ4sWLG6mFRFSQXbx4Ea1atcLNmzdhY2NjlDbUr18fI0aMQN++fY2yfwB4+PAhqlWrhtOnTyvHMcyJDz/8ELVr18bEiRMN0DrKCb5WEhEVPFn5TGjwir9Dhw7B398fZcqUUf7aLz0hBKZMmYIyZcrAwsICvr6+mbpPICIiIiIiIiIiMgYfHx/MnTsXMTExRtn/o0eP0KNHD/Tp08co+1coXbo0Vq1ahdu3b+d4W8nJyahZsyZGjhxpgJYRERGRNgYP/hISElCzZk0sXbpU7fy5c+di4cKFWLp0KSIjI+Hs7IzWrVvj5cuXhm4KERERERERERFRlg0YMAA+Pj5G2XepUqXw1VdfQZIko+w/vc6dO6t0N5pd5ubm+Prrr7WOr0hUVMTGJ+FYVBxi45OM3RQqKOLvAdGH5P8S6aGYoTfYvn17Zd/7GQkhsGjRIkyaNAndunUDAKxZswalS5fGhg0bVPp5JyIiIiIiIiIiIiIqLDZH3saE8ItIE4BMAkK6+aBXPXdjN4vyszM/A9u/BEQaIMkA/8VAHcOP9UyFi8Er/rSJjo7GgwcP0KZNG+U0c3NzNG/eHMeOHdO4XnJyMl68eKHyR0RERERERERERERUEMTGJylDPwBIE8DE8Eus/CPN4u+9C/0A+b/bR7Dyj3QyeMWfNg8ePAAg7yM8vdKlS+PWrVsa1wsJCcHUqVNztW1ERMbkMX6nsZtAVGjFzO5g7CYQERERERFRERcdl6AM/RRShUBMXCJcbNkNLqnxNOpd6KcgUoGn/wG2rsZpExUIeVrxp5Cxj3IhhNZ+yydMmID4+Hjl3507d3K7iURERERERFSApaWl6V6IiIioCOJrpHF4OlpBluErcBNJgoejpXEaRPmfvZe8e8/0JBPAvrxx2kMFRp5W/Dk7OwOQV/65uLgopz969ChTFWB65ubmMDc3z/X2ERERERERUcFmZmYGmUyG+/fvw8nJCWZmZlp/aEpERFRUCCHw5s0bPH78GDKZDGZmZsZuUpHiYmuBkG4+mBh+CalCwESSMKtbdVb7kWa2rvIx/baPkFf6SSaA/yJW+5FOeRr8eXp6wtnZGXv37kXt2rUBAG/evEFERATmzJmTl00hIiIiIiKiQkgmk8HT0xOxsbG4f/++sZtDRESU71haWsLd3R0ymVE6gyvSetVzRzNvJ8TEJcLD0ZKhH+lWJwDwainv3tO+PEM/0ovBg79Xr17h5s2bytvR0dE4d+4c7O3t4e7ujhEjRmDWrFmoWLEiKlasiFmzZsHS0hJ9+/Y1dFOIiIiIiIioCDIzM4O7uztSUlKQmppq7OYQERHlGyYmJihWrBir4Y3IxdaCgR9lja0rAz/KEoMHf6dOnYKfn5/y9qhRowAAAwYMQFhYGL766iskJSVh6NChePbsGRo0aIC//voLNjY2hm4KERERERERFVGSJMHU1BSmpqbGbgoREREREVGeMXjw5+vrCyGExvmSJGHKlCmYMmWKoXdNRERERERERERERFSoxMYnITouAZ6OVqwWzE/i7wFPowB7L1bkUb6Sp2P8ERERERERERERERGRfjZH3saE8ItIE4BMAkK6+aBXPXdjN4vO/Axs/xIQaYAkA/wXy8fjI8oHOIIrEREREREREREREVE+ExufpAz9ACBNABPDLyE2Psm4DSvq4u+9C/0A+b/bR8inE+UDDP6IiIiIiIiIiIiIiPKZ6LgEZeinkCoEYuISjdMgknsa9S70UxCpwNP/jNMeogwY/BERERERERERERER5TOejlaQSarTTCQJHo6WxmkQydl7ybv3TE8yAezLG6c9RBkw+CMiIiIiIiIiIiIiymdcbC0Q0s0HJpI8/TORJMzqVh0uthZGblkRZ+sqH9NPMpHflkwA/0Xy6UT5QDFjN4CIiIiIiIiIiIiIqLCLjU9CdFwCPB2t9A7vetVzRzNvJ8TEJcLD0ZKhn6HF35N33WnvlbXgrk4A4NVS3r2nfXmGfpSvMPgjIiIiIiKiPBMSEoLw8HBcvXoVFhYWaNy4MebMmYNKlSoZu2lEREREuWZz5G1MCL+INAHIJCCkmw961XPXa10XWwsGfrnhzM/A9i/l4/VJMnkVX50A/de3dWXgR/kSu/okIiIiIiKiPBMREYHPP/8c//zzD/bu3YuUlBS0adMGCQkJxm4aERERUa6IjU9Shn4AkCaAieGXEBufZNyGFWXx996FfoD83+0j5NOJCjhW/BEREREREVGe2b17t8rt0NBQlCpVCqdPn0azZs2M1CoiIiKi3BMdl6AM/RRShUBMXCIr+YzladS70E9BpMq77mQVHxVwDP6IiIiIiIjIaOLj4wEA9vb2GpdJTk5GcnKy8vaLFy9yvV1EREREGWVnjD4A8HS0gkyCSvhnIknwcLTMhVaSXuP22XvJu/dMH/5JJvLx+ogKOHb1SUREREREREYhhMCoUaPw/vvvo3r16hqXCwkJga2trfLPzc0tD1tJREREJB+jr8nsA+j70wk0mX0AmyNv672ui60FQrr5wESSAMhDv1ndqrPaLzec+RlYVB1Y4y//98zP6pezdZWP6SeZyG9LJoD/Ilb7UaHAij8iIiIiIiIyimHDhuHChQs4cuSI1uUmTJiAUaNGKW+/ePGC4R8RERHlGU1j9DXzdtI7vOtVzx3NvJ0QE5cID0dLhn65QdO4fV4t1Qd6dQLk857+J6/0Y+hHhQSDPyIiIiIiIspzX3zxBf744w8cOnQIZcuW1bqsubk5zM3N86hlRERERKoMNUafi60FA7/clJ1x+2xdGfhRocOuPomIiIiIiCjPCCEwbNgwhIeH48CBA/D09DR2k4iIiIi0UozRlx7H6MuHFOP2pcdx+6gIYvBHREREREREeebzzz/HunXrsGHDBtjY2ODBgwd48OABkpKSjN00IiIiKgJi45NwLCoOsfH6v/fgGH1GFn8PiD4k/1cbjttHBIBdfRIREREREVEeWrFiBQDA19dXZXpoaCgCAwPzvkFERERUZGyOvK0cq08mASHdfNCrnrte63KMPiM58/O7cfskmTzYqxOgeXmO20fE4I+IiIiIiIjyjhBC90JEREREBhYbn6QM/QAgTQATwy+hmbeT3iFebo7RFxufhOi4BHg6WhXtUDH+nnysPnsv+W1F6AfI/90+Qh7saQv0OG4fFXEM/oiIiIiIiIiIiIjyGQZBhhUdl6AM/RRShUBMXKLRz29OKhELBUXYd/8csC/4XXVfo8/fhX4KIlVezcdgj0gjBn9ERERERERERERE+UiRD4JygaejFWQSVMI/E0mCh6Ol8RoFw1QiFmjpu/JMT6QBx5cBkACku2iSibwLTyLSSGbsBhARERERERERERGRnKYgKDY+ybgNK+BcbC0Q0s0HJpIEQB76zepW3ejhmrZKxEIv/p760E9BpAGNv5CHfYD8X/9FrPYj0oEVf0RERERERERERET5RH7ukrKg61XPHc28nRATlwgPR8t8cT7zayVinngapTn0A+RBX4NP5X9P/5NX+jH0I9KJFX9ERERERERERERE+YQiCEqvyARBecDF1gKNvBzyRegH5N9KxDxh7yUfy0+d9NV9tq6AZ1OGfkR6YsUfERERERERERERUT6hCIImhl9CqhBFKwgqovJjJWKesHUF/BcD20cAIlUe9rUKBsrUYXUfUQ4w+CMiIiIiIiIiIiLKR4psEJRPxMYnITouAZ6OVnl27l1sLQrudY6/J++2094r62FdnQDAqyW78iQyIAZ/RERERERERERERPlMgQ6CCrDNkbcxIfwi0gQgk4CQbj7oVc/d2M3Kv878DGz/Uj5WnySTV/DVCcjaNhTdeRKRQXCMPyIiIiIiIiIiIiIq8mLjk5ShHwCkCWBi+CXExicZt2H5Vfy9d6EfIP93+wj5dCIyGgZ/RERERERERERERFTkRcclKEM/hVQhEBOXaJwG5XdPo96FfgoiVd5tJxEZDYM/IiIiIiIiIiIiIiryPB2tIJNUp5lIEjwcLQHIKwKPRcUZrALQ0NszmLungWNL5f9qY+8l794zPclEPlYfERkNx/gjIiIiIiIiIiIioiLPxdYCId18MDH8ElKFgIkkYVa36nCxtTD42H/5dizBrZ8B5ze8u12zL9B1hfplbV3lY/ptHyGv9JNMAP9FHK+PyMgY/BERERERERERERERAehVzx3NvJ0QE5cID0dLuNhaaBz7r5m3E1xsLbK8D0Nvz2DunlYN/QD57XqDgbLvqV+nTgDg1VLevad9eYZ+RPkAgz8iIiIiIiIiIiIiov9zsbVQCeC0jf2XnaDO0NvLlvh78jH67L3ehXW3j6tf9s4/moM/QL4+Az+ifIPBHxEREREREREREREZTWx8EqLjEuDpaGXcijcNFGP/pQ/r0o/9l1UX78ZnmpaT7elNEfbdPwfsCwZEmnyMPv/F8so990bq13NrmLvtIiKDYvBHREREREREREREREaRb8e6S0fb2H9ZFRufhDm7r2aa/lX7Srkbep75Gdj+pTzsS0+kycfo82opr+qr2TfzGH/aqv2IKN9h8EdERERUAHmM32nsJhAVajGzOxi7CURERESFXr4d604NdWP/ZYe6bj4BoIZryZw1UJv4e+pDPwWRKh+jz9YV6LpCPqbfnX/klX4M/YgKHAZ/RERERERERERERJTn8sVYd1mQcey/7DB0t6F6eRqlOfQDAMkEsC//7nbZ9xj4ERVgMmM3gIiIiIiIiIiIiIiKHkUIll6ejHVnRIpuQ00k+YHnpNtQvdl7ycfyU0cyAfwXyav9iKhQYMUfERERERERERERUREXG5+E6LgEeDpa5Vm1nSHHzitIDNJtaPw9eSWfvZfu0M7WFfBfLB/LT6TKw75WwUCZOvJKP4Z+RIUKgz8iIiIiIiIiIiKiImxz5G3lWHsyCQjp5oNe9dzzZN+GGjuvoMlRt6Fnfn43Zp8kk4d6dQK0r1MnAPBqKR/Lj2EfUaHGrj6JiIiIiIiIiIiIiqjY+CRl6AfIx56bGH4JsfFJedYGF1sLNPJyKDKhX47E33sX+gHyf7ePkE/XxdYV8GzK0I+okGPwR0RERERERERERFRERcclKEM/hVQhEBOXaJwGkXZPo96FfgoiVV7JR0QEBn9ERERERERERERERZanoxVkkuo0E0mCh6OlcRpE2tl7ybv3TE8ykXffSUQEBn9ERERERERERERERZaLrQVCuvnARJKnfyaShFndqrPbzfzK1lU+pp9kIr8tmQD+i9h9JxEpFTPGTlNSUjBlyhSsX78eDx48gIuLCwIDA/H1119DJmMWSURERERERERERJRXetVzRzNvJ8TEJcLD0ZKhX35XJwDwainv3tO+PEM/IlJhlOBvzpw5+P7777FmzRpUq1YNp06dwsCBA2Fra4svv/zSGE0iIiIiIiIiIiIiKrJcbC0Y+BUktq4M/IhILaMEf8ePH0fnzp3RoUMHAICHhwc2btyIU6dOGaM5RERERERERERERERKsfFJiI5LgKejVc4C0fh7wNMo+dh8DOqIKA8YJfh7//338f333+P69evw9vbG+fPnceTIESxatEjt8snJyUhOTlbefvHiRR61lIiIiIiIiIiIiEh/BguMyGg2R97GhPCLSBOATAJCuvmgVz33rG/o6GJgbzAAAUgy+dh8dQIM3l4iovSMEvyNGzcO8fHxqFy5MkxMTJCamoqZM2eiT58+apcPCQnB1KlT87iVRERERERERERERPozWGCURfk9bMzv7UsvNj5JeQ0BIE0AE8MvoZm3k/a2x98D7pyQ/9+tAXBpC7B38rv5Ig3YPkI+Nh8r/4goFxkl+Nu8eTPWrVuHDRs2oFq1ajh37hxGjBiBMmXKYMCAAZmWnzBhAkaNGqW8/eLFC7i5ueVlk4mIiIiIiIiIiIg0ynZglEPGChv1ld/bl1F0XILyGiqkCoGYuETN1/HMz8AfwwGkX1HKvJxIBZ7+x+CPiHKVUYK/sWPHYvz48ejduzcAwMfHB7du3UJISIja4M/c3Bzm5uZ53UwiIiIiIiIiIiIivWQrMMohY4WN+srv7VPH09EKMgkq19JEkuDhaKl+hfh7wPYvoRr6Qc1tAJAB9uUN1FIiIvVkxthpYmIiZDLVXZuYmCAtLc0YzSEiIiIiIiIiIiLKEUVglJ7WwMgAtIWN+UF+b586LrYWCOnmAxNJfjFNJAmzulXXHFQ+jZJ346mP1lNY7UdEuc4oFX/+/v6YOXMm3N3dUa1aNZw9exYLFy5EUFCQMZpDRERERERERERElCOKwGjClotIg7ziQmtgZABZrk7LY/m9fZr0queOZt5OiIlLhIejpfwaxt+Th3z2Xqrhnb0XIMnUhH8SIEny6ZIMaDUVaDI8T4+DiIomowR/3333Hb755hsMHToUjx49QpkyZfDJJ59g8uTJulcmIiIiIiIiIiIiyq8kyHt5VDPEm6EpwsaJ4ZeQKoTu6rQ8lt/bp42LrcW7dp75Wd6dpyLE818M1AmQz7N1ld/ePhwQioRTAjotAbxaysf0sy/PSj8iyjNGCf5sbGywaNEiLFq0yBi7JyIiIiIiIiIiIjIoY41np7Y6LR/J7+3TSTGGn6KiT6QB20fIQz1FmFcnQH77zkn5bbf67+Yx8COiPGaU4I+IiIiIiIiIiIioMNE2nl1uh10q1Wn5UFbaFxufhOi4BHg6WmVaR9u8bFN04WlqBbxNyNyVp7ox/ESqvJIv/XK2roBtV8O0iYgoBxj8EREREREREREREeVQQR3PLj/ZHHlbWTUpk4CQbj7oVc9d57xsib8HnFgBHFsKed+s/5exK091Y/hJJvLuO3MgV0JMIiLIx5glIiIiIiIiyjOHDh2Cv78/ypQpA0mSsG3bNmM3iYiICqDY+CQci4pDbHySsZsC4N14diaSfHC/gjSeXX6gqavU2PgkrfOyLP4e8NfXwLfVgGPfQSX0A9515Rl/T35bMYafZCK/LZkA/oty1IXn5sjbaDL7APr+dAJNZh/A5sjb2d4WEVFGrPgjIiIiIiKiPJWQkICaNWti4MCB6N69u7GbQ0REBZDBq78MxFjj2elTPZbfK8y0dZUqILLfjerd08D13YB1aXlXnvumZO66M6OMXXkqxvB7+p+80i8HoZ+6EHPClou5PhYkERUdDP6IiIiIiIgoT7Vv3x7t27c3djOIiKiA0lT9lV+Ck7web0+fEDS/BqXp6eoqNTvdqL752hamJsD/izD1p64rT1vXHAV+CuoCzjQAoUdiMLFDlRxvn4iIXX0SERERERERERFRgaGtMqyo0acLTIN2k5mLtHWVmuVuVOPvIW1yDkI//0WIhX2udCXr6WgFdU1aeeS/fHdNiKhgYsUfERERERER5WvJyclITk5W3n7x4oURW0NERMamqzKsKNEWgipCMX2WyS+0dZWqmHc65hkgAe+Vs3u3Yvw94GkUYO8FRO1H2u9fQKZ3yYsENP4CqNoFeJsI2JfH5uupmDD7QK5USLrYWmBIU0/8eDhaZXqaQL68JkRU8DD4IyIiIiIionwtJCQEU6dONXYziIgon1BUf00Mv4RUIXRXfxUy6cfq0ycELWhBqbauUg9df6ysXiwjPcHMZpbwK3Ef2BcsH7dPkgFCQKZPlZ8kAxoNAxp8qtKFp7xC8kCudiU78H1PrDwSXWCuCREVLAz+iIiIiIiIKF+bMGECRo0apbz94sULuLm5GbFFRERkbNoqwwozdWP16QpBDRGUpg8bjXWuY+OTsDj8IBpID1Bd9h/GF9sEkxMCAnjXdaZI07oNIQCpzXSgTG35GH5qxuzLiwrJoh5eE1HuYvBHRERERERE+Zq5uTnMzc2N3QwiIspntFWGFUaaxuo7Mt4PR8b7aQ1BcxKUqgsbDdXtpV7+341n8sWjOGw2ByaSkAd4/0/79CnuE0L+Jxt9WW3Yl15eVUgW1fCaiHIfgz8iIiIiIiLKU69evcLNmzeVt6Ojo3Hu3DnY29vD3T0Pv0gkIiIqQLRVojXyclAuA0BtiKQpKNVWzacpbDRkt5dqKcbs+y8COLIAEALlkC7s05b2SRIgJABpSBUA0oA3bwGL2fF67Tovq/GKWnhNRHmDwR8RERERERHlqVOnTsHPz095W9GN54ABAxAWFmakVhERUUGRH7qdNAZtlWjZrcrTtl5sfBJ2XLif691eZrJ/OnB4fqbJ+lT2QTIB/BcBXi2Bp//B5P/deWa1pazGI6KCjMEfERERERER5SlfX18IIXQvSERElIHRu53MgZwGlpoq0QDoVZWXcf/aqvkOXX+sMi89g3d7efc0cH03YF0auLEHuPGXXqspuvsUkgmkVsFAmTqq4/bp6NJTl7yuxiuqgTYRGR6DPyIiIiIiIiIiIspX1IUgRut20gB+OBSF2buuyseZy0Fgqa4S7VhUnM6qPHWBqZu9pdr1Tsc80xr6Gazby/h7QPgQ4NZRvVdRhH0pQoY5Kb3xr/DCt0O7onRZr5y3x4gKcqBNRPkPgz8iIiIiIiIiIiLKNzSFINrGuDN28KetWuuHiCiE7LqqvJ3TwDJjJZq2LkAVbVMXmIYPbaR2PWSYpvBNhyr4oIZLzs61Yuy++2eBvZOzvPrlCkMw84oz/ksrhceSI2Z1q47SZQt2QFaQA20iyp8Y/BERERERERUhq1evRlBQkMb5L1++xMiRI7Fy5co8bBUREZGcthBEV8BlLLrGyZudLvRTMGRgqakLUMW2NQWmiW/SVNaTSUDQ+x5ws7NQe56zGvqphKEvLwPHvwP+3ZrNo5QBraegWpMvsSA+qVCNvZefA20iKpgY/BERERERERUhI0eORHh4OFauXAlnZ2eVeXv27MGQIUNgZ2dnpNYREVFRpy0EaeTloDXgMgZd1VrRcQlQN6qtTIJBA0t1XYAqaAtMG3k5oJm3E0KPRuOnQ9H46XA0Vh2JRtfarth29n62z/Mfh05i0+6D+C/NGWOK/YLuxQ5Dys6BVWwLNP5COXZfYRwHL78G2kRUcDH4IyIiIiIiKkLOnz+PgQMHolq1ali6dCn69OmDly9fYsSIEVi3bh3Gjh2L4OBgYzeTiChHCmM4UFToCkG0BVzGoKtaS93xAMC49pUN3vaMXYCmn64rMF15OFoZUKYJYNvZ+wgf2giJb9Kydp7vnkbSoUXocO0PdDIDUgUgA7IW+jUdA1jaA24NgbLvKScX1nHw9Lk+RERZweCPiIiIiIioCPHw8MDff/+NRYsWYciQIVi/fj0uXryIEiVK4NixY3jvvfd0b4SIKB8rrOFAUaAIbMe1q4y5u69pDEE0BVzG4OloBQlQqepLH1RmDHVkkId+nzTzytN2agtMtXUF2sjLQffGFeP2HZoHRB+CBaBM+kyykvj59ARaTQFsXTPNyi/j4OXWjwryW6BNRAUbgz8iIiIiIqIi6JNPPsGhQ4ewbds2WFlZ4Y8//kDNmjWN3SwiohzJL+EAZV3GwHZc+8qo4VoyX4Yg6cOfQ9cfq8yTgExBZcZQBwCORcXleUWqpsA0W11Nxt8D7pwAoiOA02sAtR2aaiMBracBtm7ym2711QZ+CvlhHLzc/lFBfgq0iahgY/BHRERERERUxBw9ehQDBw6Eqakpdu/ejZUrV6JRo0aYOXMmRo4caezmERFlW34IByjr1AW2c3ddw5HxfvnuumUMf4RQjbwkCWjm7ZRpPUWok58qUtMHmJq6msxU4Xb3NHD8O+DfrXrvJ03IA1FJUf3n1RLo9J3WoC8jY4+Dxx8VEFFBwuCPiIiIiIioCBk9ejSWLl2KYcOGYdasWTA3N0ebNm2wefNmDBs2DFu3bkVYWBjKly9v7KYSEWWZscMByp6CEtiqC38yShPQ2G5d4VFejk2pLoA8Mt5PpavJ9MuUkZ5gi+tGuMQdy9J+UgUwIWUIrqe5Y03rNNh6N1UZt09fxh4Hr6DcR4mIAAZ/RERERERERcrvv/+Offv2oWnTpirTe/XqBV9fX3zyySeoWbMmXr58aaQWEhFln7HDAcqeghLYqgt/MtLWbm3h0aHrj/OsElBTAHlkvJ9yTL+Hd6Pw+9YtKCWc0czkAkKK/QSTOP33IQCcSa2Az99+iceSI2Z1qw5bPY9HUwBqzHHwCsp9lIgIYPBHRERERERUpJw/fx5WVlZq55UuXRrbtm3D2rVr87hVRESGY8xwwJDysvorL2g7noIS2KoLfyQJkASQBuhst6bwyNJMlqfdSGqtXnt5Gdg/DaWiD2KDGZAqJEgQkEnqt6WJVLEtynRcg2+z+DjU1RWqscbBM/Z9tLA9HxBR7mLwR0REREREVIRoCv3S69+/fx60hIgo9xgrHDCU/DQOnCHoczwFIbDVFP7o225N6ye8SdXajaS+oY++y2UMIJ3xBF6yh6h1eDUQsw+AfEw+ADCRdJQ4KpZu/AVQrgnwNApwawiUfQ8u/z9mfeX3cfSMdR8tbM8HRJT7GPwRERERERERERHlE/k9/MiqrBxPQQhsNYU/+rZb3fqx8Ukau5HUN/TJSjiUPoDsLjuAkGIr5QFfTBZPRrkmQL0hgFt9wNY1iytnVhDG0cvr+2hhez4gorwhM3YDiIiIiIiIiIiISE5b+FEQFbbjAeThTyMvB53BS2x8Eo5FxSE2Pknr+oogzkSS19kpKgEBqA19Mm5PUziUcTkAQPw9IPoQenmb4NjnlTDHdJXOqr40AaQIedsEJKBaN2DwAWDgn0D1rgYJ/YB3lYjpFfVx9Arj44eIch8r/oiIiIiIiIiIiPIJTePAFdTwo7Adjzbpu9o8dP1xlrpnVFcJeCwqTq8KOL0r5fZPAw4vkP9fkqF0o88hH51QMyGApSldsCG1JcrLHuHboV1RuqyXPqcjy4w9jl56+WVMvaL0+CEiw2HwR0RERERERERElE/kp/BDF33CkYJ0PDmRsatNIQBFVqNv94wZu5HUN/TRtFx58+dA9L+AqRWw9xvg1tF3C4g04NgyQJLJ/6+GAPBnagMsTO0JE0nCyK6+KF02d8eWyw9jPebmmHpZDRSLyuOHiAyLwR8REREREVERceHCBb2XrVGjRi62hIiItMkP4YcuWQlHCsLx5IS6rjYzys5YdfqGPuqW21j3Okqv6qcx1Pt/S4FGw4HjywCRqjrL0xdSy8moY1MVG/P4uhlzrMfcHFMvu4FiYX/8EJHhMfgjIiIiIiIqImrVqgVJkiCE+rF8FPMkSUJqaqraZYiIKG8YM/zQRFGtZGVmkuVwJD8ejy76Vmep62ozo+x2z6hv6NPL2wRt29/Ci8d3YVW+Phz+mKoj9JOP13fauSfcBgWi9Nv7gKkl8DYRsC+vHLfPBShw1y0n9O42NYtyGigWxMcPERkPgz8iIiIiIqIiIjo62thNICKiAip9tZKEd91YKhgiHMlr2oI9faqz0gehGbvalCRAEvIR9HLaPaPa0Cf+HnDnxP//fxfY+w1KAigJABd1b1MAWPq2ExZsuG3w7iwLstwaUy+3AkUiInUY/BERERERERUR5cqVM3YTiIioAMpYraSuuM0Q4Uhe0hbs6VOdlXH9rrVdse3sfZUuOXOte8YzPwN/DIf6K6GbAPBnSgMsSO0FwLDdWRZ0uTWmXm4FikRE6jD4IyIiIiIiKsIuX76M27dv482bNyrTO3XqZKQWERFRfqOpK0tFkGGocATQv3vNnO5DW7CnqzpL3frbzt5H+NBGSHyTphL0GewYFBV+iU+BP8dAv9AvQ22mJAOqdsEFt4/w+bbXKkumCoEzt57Bzip3z31BkBtj6uVWoEhEpA6DPyIiIiIioiLov//+Q9euXXHx4kWVcf8kSQIAjvFHRERKmqqV1AVdOaFP95qGoCvY01WdpWn9xDdpaOTloHXfWQ42754GDs0Fru/W59BU9dkEmFllGruvVHwSZL8fyNQ16bANZyHw7tw383ZSthVArgey+UlujKmXG4EiEZE6DP6IiIiIiIiKoC+//BKenp7Yt28fypcvj5MnT+LJkycYPXo05s+fb+zmERFRPqKpWqmmm53B9qFP95qK5XIaQOkK9nRVZ2W320a9g01FdV/kT8CtY1k+PgFAqtkXqNRO7fyMxyeTACHe1QamCWD8louQ/n+MUrrtcjzAnMmNQJGIKCMGf0REREREREXQ8ePHceDAATg5OUEmk0Emk+H9999HSEgIhg8fjrNnzxq7iURElI/kdrWSrio8wHAVgfp0u6jteLPTbaPWYBNP5UEfAMTfBfZORpbG75MknK00Er9deAZH6TkOptVG37Jd0UvLKumPL+7Va3yx8ZzKfAF5GKj4v0J2xwPMiy5c80JhOQ4iKtwY/BERERERERVBqampsLa2BgA4Ojri/v37qFSpEsqVK4dr164ZuXVERJQf5Wa1kq4qOk3BWWVnGyS8Sc1yEKMryIyNT8KpmKeQNFTyZTUI1RRsip1fAdd/1rvd70jABwsAS3s8LFkD3ZddVdn+JT3COcX1jI1PynTutckYyOqSV1245rbCchxEVPgx+CMiIiIiIiqCqlevjgsXLqB8+fJo0KAB5s6dCzMzM/z4448oX768sZtHRERFjK4qOk3BWZflxyCyGcRoCjI3R97G+C0XlZVuEoDZ3TNvOytBqJWZCSS8q55zxhOsN5sFl+uxerf3HQnotASoEwAAiIqK01ktqU2mrj//305NOaA+3Zoq6NuFa35XWI6DiIoGBn9ERERERERF0Ndff42EhAQAwIwZM9CxY0c0bdoUDg4O2Lx5s5FbR0RERZG2Kjp1FYHAu+4oDRXExMYnqYR+gDwAmxB+MdvbVlSKlcYTeMoeoLr0H8YX2wgTSfe6mbw3EGg2FrB1VU7K7piDCrHxSXCzt0T40EZIfJMGD0dLHLr+WBkESv9PLMX/t6urW9P09OnCtSAoLMdBREUDgz8iIiIiIqIiqG3btsr/ly9fHpcvX8bTp09hZ2cHScrON5FERPkfx+fK/zRV0amrSkvLsIwhgpjouAS1lW5pAtna9sO7Ufh96xYMkkX/P+wTEALI0kutdzugQhugUjuVwE8hO2MOKqjrvrKRl0OmEBZAtsZ3zGkomV8UluMgoqKBwR8REREREREBAOzt7Y3dBCKiXMPxuQq+9GGUpZkMXZcfM3gQ4+lopdIlp4JMgn7bjr8H3Dnx///fQam9U7DBLE0l7NMZ+rWeBtj+/77pVl9t2JeRPmMOZgy+dXVfmTGEzU6gmpNQMj8pLMdBREWD0YK/e/fuYdy4cdi1axeSkpLg7e2NVatW4b333jNWk4iIiIiIiIqMhIQEzJ49G/v378ejR4+QlqZaN/Hff/8ZqWVERIbH8bkKj/RhVG4EMS62Fpjd3Ud1jL//B8WKsExt1Wj8PeDECuDYUqSPDaV029DJvgIw4A+9gj5Nbdd0/OqCbzd7yzzpvlKfULIgKCzHQUSFn1GCv2fPnqFJkybw8/PDrl27UKpUKURFRaFkyZLGaA4REREREVGRM3jwYERERKB///5wcXFh955EVKhxfK7CKbeCGMV2T8c8gyQBdcrZwcXWIlN49r0f0MY6Gnh+Gzj5Q5b2IfAuFIRHU6DRMHlXnrlAU/AdPrRRnnVfqS2UzGs56fLXEMfBLoeJKLcZJfibM2cO3NzcEBoaqpzm4eFhjKYQEREREREVSbt27cLOnTvRpEkTYzeFiCjXFYbxuRgWqJdbgZKLrQU61ny33Yzh2Y8mc9Hy6Ll06Z1uiu4+U4QMc1N6o2HTVmjRqKHOCr+cXntNwXfim7Qi132lsbv8Nfb+iahoMErw98cff6Bt27b48MMPERERAVdXVwwdOhRDhgxRu3xycjKSk5OVt1+8eJFXTSUiIiIiIiqU7OzsOKYfERUZBX18LoYFqowRgt67dRMNpH8RLZwxo9gqtDQ5p1f3nYrKvhQhw5yUXrgovBCTVhoP4IBVERKONLKHi5b1DXHttQXfjbwcikz3lcbu8tfY+yeiosMowd9///2HFStWYNSoUZg4cSJOnjyJ4cOHw9zcHAEBAZmWDwkJwdSpU43QUiIiIiIiosJp+vTpmDx5MtasWQNLy4JT8UJElF0FdXwuhgWq8jQEjb8HPI0C/ovAe4cXYKOZQJqQIEHoN2YfJEitp+HAS1d8HZGA+8JBZa6u7mYNde11Bd/5oRvOvAhzjd3lr7H3T0RFh1GCv7S0NNStWxezZs0CANSuXRv//vsvVqxYoTb4mzBhAkaNGqW8/eLFC7i5ueVZe4mIiIiIiAqbBQsWICoqCqVLl4aHhwdMTU1V5p85c8ZILSMiyj35IeDIKoYF7+RpCHrmZ2D7l4BIA/CuR0+ZJDSvo+DTE6j0AeBWH7B1RQsAK6o9Q5dlx5B+bV3dzRry2ufn4Duvwlxjd/lr7P0TUdFhlODPxcUFVatWVZlWpUoVbNmyRe3y5ubmMDc3z4umERERERERFQldunQxdhOIiEgPBTUsyI0KrlwLQRWVffZe8vH24u+phH56k2RAq6lAk+GZZtV0s8Ps7lnrbtbQ1z4/Bt95GeYau8tfY++fiIoOowR/TZo0wbVr11SmXb9+HeXKlTNGc4iIiIiIiIqc4OBgYzeBiIj0UBDDgtyq4MqVEDR9ZZ8kA/wXA3YeWkM/8f/9S9L/x/DzaA40HwvYl5cHhxpktequIF77rMrrilZjVz4ae/9EVDQYJfgbOXIkGjdujFmzZqFnz544efIkfvzxR/z444/GaA4REREREREREVG+VZDCgtys4DJYEBZ/D7hzAkh8Cuwa+y7kE2nA9hHAoL3yEFBN+CcEMCulL/5JrYz6JjfwaUBfOFVqnKVjyEp7s3LtdVVZ5sU4ellljIpWY1c+Gnv/RFT4GSX4q1evHrZu3YoJEyZg2rRp8PT0xKJFi9CvXz9jNIeIiIiIiKhIsLe3x/Xr1+Ho6Ag7OztIkqRx2adPn+Zhy4iISJeshAXGDHhyu4Ir2yGoojvP/w4ChxdoXk6kAm8T5ZV/20fIb/9fGiTMTumDn1I7wkSS8FGXrnCqZLix6DRdN32uva4qy7waRy+rikJVIxFRXjNK8AcAHTt2RMeOHY21eyIiIiIioiLn22+/hY2NDQBg0aJFRm3L8uXLMW/ePMTGxqJatWpYtGgRmjZtatQ2EREVBsYOeDRVcFmayXAsKs4gYWSWK6aOLgH2TX7XR6c2kom8y07PpoBXS+Dpf4CpJfA2ETL78hgIe/jlQuVlTq6brirLvBxHLzsKUkUrEVFBYLTgj4iIiIiIiPLWgAED1P4/r23evBkjRozA8uXL0aRJE/zwww9o3749Ll++DHd341cfEBEVVPkh4FFXwdWldhl0XX7MOGHk0cXA3sn6LSuZAP6L3o3TZ+uaacw+F8Dg5zKn101XlWVej6OXHez+kojIcBj8ERERERERFUEvXrxQO12SJJibm8PMzCzX9r1w4UIMGjQIgwcPBiCvPtyzZw9WrFiBkJCQXNsvEVFhpyng2XkhFh1quORZsJK+gsvSTKYM/YBcDCMV4/YBgFsDeWAXfw/YG6zHyhLQIxRwq58p6MsJfbtczWkwp2ucPGOMo0dERMbD4I+IiIiIiKgIKlmypNYx/sqWLYvAwEAEBwdDJpMZbL9v3rzB6dOnMX78eJXpbdq0wbFjx9Suk5ycjOTkZOVtTaElEVFRpy7gAYAZO69g1p9X8rTSTlHBdSwqLveqzRTj9t0/+/+AT7EjCei0BLDzSDdNi05LgOpds7x7bcFeVrruzGkwp2ucPI6jR0RUtDD4IyIiIiIiKoLCwsIwadIkBAYGon79+hBCIDIyEmvWrMHXX3+Nx48fY/78+TA3N8fEif9j777jm6r3P46/0z2AQlvogEJLFUQZshRQgQoilSFOUC9DcaCCIupV8MdyFRUVBUVUhrjgqoAyBWTpBRFBrqKAsiyrsotALdB+f3/UxKZJ26Qrbfp6Ph55YE6+5+RzTk5iTt/5fr8jSux5jxw5oqysLEVFRdktj4qKUlpamtN1UlJSNHbs2BKrAQC8Vd6AJzdPzetWKr3N0vdLa16SNs6Q82DPSF88LN29XLL4SCbbsYnFR2rRX2r/uNNefgfTM/T9nmOyWCxqWa+GW8Geu0N3lkQwV9g8ecyjBwCVB8EfAAAAAFRC7733nl5++WXdeuuttmU9e/ZUkyZNNGXKFH311VeqW7eunnvuuRIN/qzy9jY0xuTbA3H48OEaNmyY7f7JkycVFxdX4jUBlY2rwxCiYrEGPAt/PKhnF261e6yoPe2Kc67kDbV8LNK/kxu6f86l75fWT5F+niel/+7CCtnSuTNSj9ek+UMlkyXJR7pqmFS/oxReP99hPWdvSNWTn/2Uu/+gxt1UeLB3UXRVnT6bpaOnMgvs5ejseLoTzDlb35XXiHn0AKByIPgDAAAAgEpo3bp1euuttxyWN2/eXOvWrZMkXXnllUpNTS3R542MjJSvr69D775Dhw459AK0CgwMVGBgYInWAVR27gxDiIonJixY3ZrG6PlFW4vd064o50reEKp367o6ceacxi3epmwjvbB4m6oH+7t2zqXvl9ZPltZOdKtuyScn3Eu4SkrsJB3bVWDYl7v23KGflNOncPicn2w99vKbk6/XG2tllHOcLLLvi2g99gUdT1eCOWfr6+/6eD8DACSp5CZqAAAAAABUGHXq1NHUqVMdlk+dOtXWm+7o0aOqUaNGiT5vQECAWrZsqWXLltktX7Zsmdq1a1eizwXAufx6Kx1Mz/BsYShR1p52vn/3pi7K8JFFOVdmb0jVFeNW6PZ31uuKcSs0e0OqDqZn6IUl22xBmMvn3KaZ0quXFCH0s0g9X/sn5AurnRMAFhL6SdLuI6edDh6abaQ9R85I+mf40rxy758s//zh1XrsJRXrvefs9Rj+2U+8nwEAdujxBwAAAACV0Pjx43XLLbdo8eLFat26tSwWizZs2KBt27bp008/lSRt2LBBvXv3LvHnHjZsmPr27atWrVqpbdu2evvtt5WamqpBgwaV+HMBcJRfb6WiDAGJ8q2487q5e67kFxS+dtul7p9z6ful+Q/L+Rx+Tlz1mBSVE64p7jKXQj5nEiJDHXrrSTk96ay9JZ0NX5p3/4yRJt3eXOGhgbZjv3bnkWK995y9HtlyLJb3MwBUbgR/AAAAAFAJ9ezZU9u3b9dbb72lX3/9VcYYJScna968eYqPj5ck3X///aXy3L1799bRo0f19NNP6+DBg2rcuLEWLVqkevXqlcrzAbBn7a1U3CEgUTEUZ143d8+V/IJC/T0EpVvn3LGdksl2rdBrnpaueNi1toWICQvWuJua2M/x9/fwmbmPY+5QNSTARze8udZh/1rUq2G3TnHfe87W95Ek3s8AgFwI/gAAAACgkoqPj9e4ceM88twPPPCAHnjgAY88N1DZ5e2tVJQhIEtb3jniKoPyuM/univ5BVst42vYtlPTHFFnn01KikzXuXW/SW1vdt47LzxRsvgUHP7Vu0K68Z0i9+7LjzXU27jnuCwWOQR4VrlDVVeOU3Hfe/mtL6lcv58BAGWL4A8AAAAAKokff/xRjRs3lo+Pj3788ccC2zZt2rSMqgLgCcUdArI0zd6Qahsu0ufvnla9W9f1dFmlqjzvszvnSkHBVu8GvurWbo1CNk7O6aV2UtK3c5T97Sj59Jwotehnv7Gw2lKP16T5QyWTJclHSkySMtKl6vWkdg9KdVqW2n7HhAWrZXxOL0ZXuHqcivvey2/98vp+BgCUPYI/AAAAAKgkLr30UqWlpalWrVq69NJLZbFYZIzj3EkWi0VZWVkeqBBAWSrOEJClJb854to3qFnuai0pFWGf3TlXnAZTm2ZKXzykKk7m6/ORZL54SJbETo4991r0kxI7Scd2SeH1S7xnX0GKEsa6epyK+95ztn55fD8DADyD4A8AAAAAKondu3erZs2atv8GgPImvzni9hw547WhRnH3uVwOEapjislYL20/lrNg0WOSk9DPyiKTE+45C/bCapdp4CeVXhhbHl+r3Mp7fQAA1xD8AQAAAEAlUa9ePUnSuXPnNGbMGI0cOVL169f3cFUA8I/85oiLjwzxXFGlrDj7XK6GCE3fLx3bKe1aLX093q1VjSyyhJef/x+5G8a6EphNWbNT4xZvkykPr5UT5epcAgAUi4+nCwAAAAAAlC1/f3/NnTvX02UAgAPrHHG+Fosk2c0R562s++yTs8vyscilfc6vV9rB9IxSrjiPfRulTwZIr14ivdfD7dAvW5Kl5+tl3qtPyjmGa3cecThm1jA2t/zC2NkbUnXFuBW6/Z31umLcCs3ekOrQZsrqnUpZlBP6SR58rfJRbs4lAECJoMcfAAAAAFRCN9xwg+bNm6dhw4Z5uhQAsON0jrhKwBoKOZl61alyMSzqh7dKv33p5ko+Ola/p/afDVVY3EWq2+Ymt0O/khiSsqAebtYwdsScLcoyJt8A2pUhQQ+mZ2jc4m0Oz1/Sr1Vxjkm5OJcAACWG4A8AAAAAKqELLrhAzzzzjNauXauWLVsqNDTU7vGHHnrIQ5UBQE7wUlkCB2t4ZM1djFybT84jw6Lu2yilrpPqtpVWj5N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      "text/plain": [
       "<Figure size 1800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "U,D,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "fig,ax = plt.subplots(2,2, figsize=(18,8)); ax[0,0].bar(x=range(3), height=D); ax[0,0].set_title(\"Singular Values\"); \n",
    "# This shows that the approximate reconstruction of X is very poor \n",
    "ax[1,0].hist(np.abs(U.dot(np.diag(D)).dot(Vt) - X).flatten()); ax[1,1].hist(np.abs(U[:,:2].dot(np.diag(D[:2])).dot(Vt[:2,:])-X).flatten()); ax[1,0].set_title(\"Roundoff error in full reconstruction of X\"); ax[1,1].set_title(\"Approximation error in compact reconstruction of X\"); ax[0,1].plot((U[:,:2].dot(np.diag(D[:2])).dot(Vt[:2,:])).ravel(), X.ravel(),'.', label='Compact Reconstruction:  X~ = (U[:,:2]*D[:2]).dot(Vt[:2,:])'); ax[0,1].plot((U.dot(np.diag(D)).dot(Vt)).ravel(), X.ravel(),'.', label='Full reconstruction:            X~ = (U*D).dot(Vt)'); ax[0,1].set_title(\"X is poorly constructed with a lower rank approximation: X is characteristically full rank\"); ax[0,1].set_ylabel(\"Original X\"); ax[0,1].set_xlabel(\"Reconstructed X\"); ax[0,1].legend(); fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {
    "id": "NP_q4L90hfJ0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X columns ARE standardized: column means [ 1.11022302e-17 -3.94129174e-17] column standard deviations [1. 1.]\n",
      "['Condition No.:' '12']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coef.</th>\n",
       "      <th>Std.Err.</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "      <th>[0.025</th>\n",
       "      <th>0.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.869406</td>\n",
       "      <td>0.092201</td>\n",
       "      <td>9.429496</td>\n",
       "      <td>2.288634e-15</td>\n",
       "      <td>0.686413</td>\n",
       "      <td>1.052399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>0.817587</td>\n",
       "      <td>0.560128</td>\n",
       "      <td>1.459643</td>\n",
       "      <td>1.476192e-01</td>\n",
       "      <td>-0.294112</td>\n",
       "      <td>1.929286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>1.289408</td>\n",
       "      <td>0.560128</td>\n",
       "      <td>2.301989</td>\n",
       "      <td>2.347431e-02</td>\n",
       "      <td>0.177709</td>\n",
       "      <td>2.401107</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Coef.  Std.Err.         t         P>|t|    [0.025    0.975]\n",
       "const  0.869406  0.092201  9.429496  2.288634e-15  0.686413  1.052399\n",
       "x1     0.817587  0.560128  1.459643  1.476192e-01 -0.294112  1.929286\n",
       "x2     1.289408  0.560128  2.301989  2.347431e-02  0.177709  2.401107"
      ]
     },
     "execution_count": 394,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The standard errors are inflated for highly multicolliner X\n",
    "n = 100; X = stats.multivariate_normal(cov=np.array(((1,.99),(.99,1)))).rvs(n); X=(X-X.mean(axis=0))/X.std(axis=0); print(\"X columns ARE standardized:\", \"column means\", X.mean(axis=0), \"column standard deviations\",  X.std(axis=0))\n",
    "X = sm.add_constant(X); Y = X.dot(np.ones(3)) + stats.norm().rvs(n); model = sm.OLS(Y,X); results = model.fit(); print(results.summary2().tables[2].values[3,2:]); results.summary2().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {
    "id": "1zoX3DiWKbb1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance Inflation Factors 1.0 36.90678381401809 36.90678381401809\n"
     ]
    }
   ],
   "source": [
    "print(\"Variance Inflation Factors\", VIF(X,0),VIF(X,1),VIF(X,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {
    "id": "kGgIvIAzhlBf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s(X^TX)^{-1/2}                   [0.09220087 0.56012906 0.56012906]\n",
      "s(VIF/(n-1)*Var[X])^{-1/2}       [0.09220087 0.56012906 0.56012906]\n",
      "\n",
      "Singular Values [14.093826028017766, 10.0, 1.167933171020049] Singular Values^{-2} [0.005034335879654118, 0.01, 0.7331013404007057]\n",
      "s*(SUM_i V_ij^2 D_ii^{-2})^{1/2} [0.09220087 0.56012906 0.56012906]\n"
     ]
    }
   ],
   "source": [
    "s = (float(results.summary2().tables[0].iloc[-1,-1]))**.5 # residual error\n",
    "XtXinv = np.linalg.inv(X.T.dot(X)); print('s(X^TX)^{-1/2}                  ', s*np.diag(XtXinv)**0.5)\n",
    "VIF_formula = np.array([VIF(X,0),VIF(X,1),VIF(X,2)])\n",
    "# This formula doesn't work for the intercept since Var(X_intercept)=0\n",
    "VIF_formula[1:] = s*(VIF_formula[1:]/((n-1)*X.var(ddof=1,axis=0)[1:]))**0.5; VIF_formula[0] = s*XtXinv[0,0]**0.5; print('s(VIF/(n-1)*Var[X])^{-1/2}      ', VIF_formula)\n",
    "U,D,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "print(\"\\nSingular Values\", list(D), \"Singular Values^{-2}\", list(D**(-2)))\n",
    "XtXinv_by_svd = (Vt.T*D**(-2)).dot(Vt) # will be the same (sans numeric error) to XtXinv\n",
    "XtXinv_by_svd_diag = (Vt.T**2*D**-2).sum(axis=1); print('s*(SUM_i V_ij^2 D_ii^{-2})^{1/2}', s*XtXinv_by_svd_diag**0.5) \n",
    "# confirming that these coefficient variances depend on the singular values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.2 Multicollinearity<br>and Variance Inflation Factors (VIFs)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "U,D,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "fig,ax = plt.subplots(2,2, figsize=(18,8)); ax[0,0].bar(x=range(3), height=D); ax[0,0].set_title(\"Singular Values\"); \n",
    "# This shows that the approximate reconstruction of X is very poor \n",
    "ax[1,0].hist(np.abs(U.dot(np.diag(D)).dot(Vt) - X).flatten()); ax[1,1].hist(np.abs(U[:,:2].dot(np.diag(D[:2])).dot(Vt[:2,:])-X).flatten()); ax[1,0].set_title(\"Roundoff error in full reconstruction of X\"); ax[1,1].set_title(\"Approximation error in compact reconstruction of X\"); ax[0,1].plot((U[:,:2].dot(np.diag(D[:2])).dot(Vt[:2,:])).ravel(), X.ravel(),'.', label='Compact Reconstruction:  X~ = (U[:,:2]*D[:2]).dot(Vt[:2,:])'); ax[0,1].plot((U.dot(np.diag(D)).dot(Vt)).ravel(), X.ravel(),'.', label='Full reconstruction:            X~ = (U*D).dot(Vt)'); ax[0,1].set_title(\"X is NOT SO poorly constructed with a lower rank approximation: X is NOT characteristically full rank\"); ax[0,1].set_ylabel(\"Original X\"); ax[0,1].set_xlabel(\"Reconstructed X\"); ax[0,1].legend(); fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EX-PokSfhtvL",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-Axb-math-pca\"></a>\n",
    "\n",
    "# 5.3 Principal Components Analysis (PCA) $X=UDV^T$ ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "[***Principal Components Analysis***](https://en.wikipedia.org/wiki/Principal_component_analysis) (***PCA***) is an ***unsupervised learning*** methodology uncovering linear structure in $X_{n \\times m}$. \n",
    "\n",
    "a ***PCA*** is computed as either\n",
    "\n",
    "$$\\underbrace{\\tilde X \\div \\sqrt{n} = U_{n \\times m}D_{m \\times m}(V^T)_{m \\times m}}_{\\text{singular value decomposition of the data matrix}}\\quad\\text{ or }\\quad\n",
    "\\underbrace{\\hat \\Sigma = (\\tilde X^T\\tilde X \\div n) = V_{m \\times m}D^2_{m \\times m}V^T_{m \\times m}}_{\\text{eigendecomposition of the data covariance matrix}}$$\n",
    "\n",
    "where the data columns of $X_{n \\times m}$ are centered and scaled by their column means $\\overline{X_{\\cdot j}}$ and standard deviations $\\hat \\sigma_{X_{\\cdot j}}$ as $\\tilde X_{\\cdot j}  = (X_{\\cdot j} - \\overline{X_{\\cdot j}}) / \\hat \\sigma_{X_{\\cdot j}}$ <font style=\"color:gray\">(unless the original scales of the data are part of the information that should be extracted)</font>\n",
    " \n",
    "This shows [the connection](https://math.stackexchange.com/questions/3869/what-is-the-intuitive-relationship-between-svd-and-pca) between ***SVD*** $X=UDV^T$ and the ***eigendecomposition*** of the  ***gramian matrix*** $X^TX = V D^2 V^T$ whose ***eigenvalues*** are the square of the ***singular values*** of $X$ and whose ***(semi-)orthonormal*** matrix $V^T$ is equal to that of the ***SVD*** and actually ***orthonormal*** for ***full rank*** $X$ (if the ***gramian*** is ***positive definite*** so all ***eigenvalues*** are ***nonnegative***)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {
    "id": "v655SVXFhyqa"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]),\n",
       " (11.0, 11.000000000000005),\n",
       " array([6.60840025, 2.65046789, 0.62719727, 0.26959744, 0.2234511 ,\n",
       "        0.21159612, 0.13526199, 0.12290143, 0.07704665, 0.05203544,\n",
       "        0.02204441]))"
      ]
     },
     "execution_count": 426,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mtcars = sm.datasets.get_rdataset(\"mtcars\"); Xtilde = (mtcars.data - mtcars.data.mean())/np.std(mtcars.data); U,D,Vt = np.linalg.svd(Xtilde/np.sqrt(Xtilde.shape[0])) # The actually PCA computation...\n",
    "# Xtilde.dot(Xtilde)/n is the sample covariance matrix for \"centered\" Xtilde \n",
    "# The trace of the sample covariance matrix is the sum of the diagonal of the covariance matrix... which is the sum of the variances.\n",
    "# - There are 11 variables and the Xtilde has been \"standardized\" so each variance is 1... so the trace is 11.\n",
    "# The sum of the eigenvalues of a square matrix equals the trace of the square matrix... the sum of the eigenvalues is thus the sum of the variances. \n",
    "np.var(Xtilde).values, (np.var(Xtilde).sum(), (D**2).sum()), D**2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.3 Principal Components Analysis (PCA) \n",
    "\n",
    "---\n",
    "\n",
    "***PCA*** is the ***SVD*** of $X_{n \\times m}=U_{n \\times m}D_{m \\times m}(V^T)_{m \\times m}$ which provides \n",
    "\n",
    "<span style=\"font-size:48px\">\n",
    "<table><tr><td><list><li><b>Principle directions</b> in $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $V_{\\cdot j}$ (columns of $V$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which are <b>semi-orthonormal</b> ($V_{\\cdot j}V_{\\cdot j}^T=1$) </li><br>\n",
    "    <li><b>Loadings (projections)</b> of $X_{i \\cdot}$ &nbsp;&nbsp;&nbsp;&nbsp; $U_{i \\cdot}$ (rows of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;onto this coordinate system &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U=XVD^{-1}$</li><br>\n",
    "    <li><b>Principle components</b> of $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U_{\\cdot j}$ (columns of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which are <b>semi-orthonormal</b> ($U_{\\cdot j}^TU_{\\cdot j}=1$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which also implies they are <b>linearly independent</b></li><br>\n",
    "    <li><b>Squared singular values</b> $\\lambda_j^2=D_{jj}^2$ giving the<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"proportion of total variance explained\" by each <br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$V_{\\cdot j}$ <b>principal direction</b>; namley, $\\require{cancel}\\lambda_j^2\\cancel{\\text{Var}[U_j]}^1$\n",
    "    </list> </td><td>\n",
    "<img src=\"https://miro.medium.com/max/596/1*QinDfRawRskupf4mU5bYSA.png\"></td></tr></table></span>\n",
    "\n",
    "The collection of $X_{\\cdot j}$ are assumed to be (likely ***standardized***) ***independent correlated random variables*** now represented by the ***standardized*** ($E[U_{\\cdot j}] = 0$ and $\\text{Var}(U_{\\cdot j}) = 1$) collection of ***observations*** $U_{\\cdot j}$ (scaled by $\\lambda_j^2$) indexed in a different coordinate system (defined by orthogonal basis vectors $V_{\\cdot j}$)\n",
    "such that the $U_{\\cdot j}$ vectors are ***uncorrelated*** (and hence empirically ***linearly independent***)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<!-- \n",
    "\n",
    "# 5.3 Principal Components Analysis (PCA) \n",
    "\n",
    "---\n",
    "\n",
    "***PCA*** is the ***SVD*** of $X_{n \\times m}=U_{n \\times m}D_{m \\times m}(V^T)_{m \\times m}$ which provides \n",
    "\n",
    "<span style=\"font-size:48px\">\n",
    "<table><tr><td><list><li><b>Principle directions</b> in $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $V_{\\cdot j}$ (columns of $V$) </li><br>\n",
    "    <li><b>Loadings (projections)</b> of $X_{i \\cdot}$ &nbsp;&nbsp;&nbsp;&nbsp; $U_{i \\cdot}$ (rows of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;onto this coordinate system &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U=XVD^{-1}$</li><br>\n",
    "    <li><b>Principle components</b> of $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U_{\\cdot j}$ (columns of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which are <b>uncorrelated and linearly independent</b></li><br>\n",
    "    <li><b>Squared singular values</b> $\\lambda_j^2=D_{jj}^2$ giving the<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"proportion of total variance explained\" by each $V_{\\cdot j}$\n",
    "    </list> </td><td>\n",
    "<img src=\"https://miro.medium.com/max/596/1*QinDfRawRskupf4mU5bYSA.png\"></td></tr></table></span>\n",
    "\n",
    "With all this in place we can confirm that the sum of the variances equals the sum of the ***squared singular values***: \n",
    "\n",
    "$$\\require{cancel}\\begin{align*}\n",
    "m = & {} \\text{Var}\\left(\\sum_j X_{\\cdot j}\\right) = \\sum_j \\text{Var}\\left( X_{\\cdot j}\\right) = \\sum_j \\text{E}\\left[ X_{\\cdot j}^2\\right] - \\cancel{\\text{E}\\left[ X_{\\cdot j}\\right]^2}^0  \\\\  \n",
    "{} = & \\sum_j \\text{E}\\left[ (U_{\\cdot -}[DV^T]_{\\cdot j })^2\\right] = \\sum_j \\text{E}\\left[  \\sum_i (U_{\\cdot i}[D V^T]_{i j })^2 \\right] = \\sum_j  (VD^2V^T)_{j j}  = \\sum_{j} V_{j j}^2D_{jj}^{2} \\text{ unfinished}\n",
    "\\end{align*}$$\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.3 Principal Components Analysis (PCA) \n",
    "\n",
    "---\n",
    "\n",
    "***PCA*** is the ***SVD*** of $X_{n \\times m}=U_{n \\times m}D_{m \\times m}(V^T)_{m \\times m}$ which provides \n",
    "\n",
    "<span style=\"font-size:48px\">\n",
    "<table><tr><td><list><li><b>Principle directions</b> in $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $V_{\\cdot j}$ (columns of $V$) </li><br>\n",
    "    <li><b>Loadings (projections)</b> of $X_{i \\cdot}$ &nbsp;&nbsp;&nbsp;&nbsp; $U_{i \\cdot}$ (rows of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;onto this coordinate system &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U=XVD^{-1}$</li><br>\n",
    "    <li><b>Principle components</b> of $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U_{\\cdot j}$ (columns of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which are <b>uncorrelated and linearly independent</b></li><br>\n",
    "    <li><b>Squared singular values</b> $\\lambda_j^2=D_{jj}^2$ giving the<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"proportion of total variance explained\" by each $V_{\\cdot j}$\n",
    "    </list> </td><td>\n",
    "<img src=\"https://miro.medium.com/max/596/1*QinDfRawRskupf4mU5bYSA.png\"></td></tr></table></span>\n",
    "\n",
    "Each column of $U$ and $X$ are linear combinations of each other...\n",
    "\n",
    "- $U_{\\cdot j} = \\left[X  V D^{-1}\\right]_{\\cdot j} = \\sum_{k=1}^m X_{\\cdot k} V_{k j}/\\lambda_j$ <font style=\"color:gray\">is a \"weighted average variable\" of the columns of $X$</font>\n",
    "- $X_{\\cdot j} = \\left[U D V^T \\right]_{\\cdot j} = \\sum_{k=1}^m \\lambda_k U_{\\cdot k} [V^T]_{k j} \\approx \\sum_{k=1}^r \\lambda_k U_{\\cdot k} [V^T]_{k j}$<font style=\"color:gray\"> is a \"weighted average variable\" of the columns of $U$</font><br>or can be a low rank approximation based on a ***compact SVD*** reconstruction\n",
    "\n",
    "and $\\require{cancel} \\text{Var}[\\sum_{j=1}^m \\lambda_j U_{\\cdot j}] = \\sum_{j=1}^m \\lambda_j^2 \\text{Var}[ U_{\\cdot j}] = \\sum_{j=1}^m \\sum_{k=1}^m  \\text{Var}[X_{\\cdot k} V_{k j}] = \\sum_{j=1}^m \\sum_{k=1}^m V_{k j}^2 \\cancel{\\text{Var}[X_{\\cdot k} ]}^1 = \\sum_{j=1}^m 1 =m $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.3 Principal Components Analysis (PCA) \n",
    "\n",
    "---\n",
    "\n",
    "***PCA*** is the ***SVD*** of $X_{n \\times m}=U_{n \\times m}D_{m \\times m}(V^T)_{m \\times m}$ which provides \n",
    "\n",
    "<span style=\"font-size:48px\">\n",
    "<table><tr><td><list><li><b>Principle directions</b> in $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $V_{\\cdot j}$ (columns of $V$) </li><br>\n",
    "    <li><b>Loadings (projections)</b> of $X_{i \\cdot}$ &nbsp;&nbsp;&nbsp;&nbsp; $U_{i \\cdot}$ (rows of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;onto this coordinate system &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U=XVD^{-1}$</li><br>\n",
    "    <li><b>Principle components</b> of $X$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $U_{\\cdot j}$ (columns of $U$)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which are <b>uncorrelated and linearly independent</b></li><br>\n",
    "    <li><b>Squared singular values</b> $\\lambda_j^2=D_{jj}^2$ giving the<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"proportion of total variance explained\" by each $V_{\\cdot j}$\n",
    "    </list> </td><td>\n",
    "<img src=\"https://miro.medium.com/max/596/1*QinDfRawRskupf4mU5bYSA.png\"></td></tr></table></span>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.14166014 -0.54567409 -0.49281905 -0.3558868  -0.55914771]]\n",
      "[[-0.14166014 -0.54567409 -0.49281905 -0.3558868  -0.55914771]]\n"
     ]
    }
   ],
   "source": [
    "i=1; X = stats.norm.rvs(size=(5,3))\n",
    "U,d,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "j=0\n",
    "print((X @ (Vt.T)[:,[j]] / d[j]).T)\n",
    "print(U[:,[j]].T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {
    "id": "1jD4ITFSwdTz"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.00609111 -1.20704628 -1.48879613 -0.61859934 -0.19793869]]\n",
      "[[-0.00609111 -1.20704628 -1.48879613 -0.61859934 -0.19793869]]\n"
     ]
    }
   ],
   "source": [
    "j=1\n",
    "print(X[:,[j]].T)\n",
    "print(((U*d)@Vt[:,[j]]).T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.3 Principal Components Analysis (PCA) \n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {
    "id": "ZNEmnhR3hynr"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mtcars = sm.datasets.get_rdataset(\"mtcars\"); Xtilde = (mtcars.data - mtcars.data.mean())/np.std(mtcars.data)\n",
    "U,D,Vt = np.linalg.svd(Xtilde/np.sqrt(Xtilde.shape[0])) # The actually PCA computation...\n",
    "# Standard PCA analyses for so called \"Principle Components\": i^th column of U from the SVD is the i^th Principle Component\n",
    "# A compact SVD approximate reconstruction of Xtilde would use 1st through i^th Principle Components\n",
    "plt.figure(figsize=(18,5)); plt.subplot(131); plt.plot(D**2,'.'); plt.plot(D**2); plt.xlabel(\"Principle Component\"); plt.ylabel(\"Singular Values of ~X\"); plt.title(\"Variation Explained by Each Principle Component\"); plt.subplot(132); p=2; plt.plot(U[:,:p].dot(np.diag(D[:p])).dot(Vt[:p,:]).flatten(), Xtilde.values.flatten()/Xtilde.shape[0]**.5, '.', label=\"Rebuild ~X with 2 PCs\"); p=4; plt.plot(U[:,:p].dot(np.diag(D[:p])).dot(Vt[:p,:]).flatten(), Xtilde.values.flatten()/Xtilde.shape[0]**.5, '.', label=\"Rebuild ~X with 4 PCs\"); p=11; plt.plot(U[:,:p].dot(np.diag(D[:p])).dot(Vt[:p,:]).flatten(), Xtilde.values.flatten()/Xtilde.shape[0]**.5, '.', label=\"Rebuild ~X with 11 PCs\"); plt.legend(); plt.xlabel(\"Rebuilt value\"); plt.ylabel(\"Original value\"); plt.title(\"Reconstructing ~X from its Principle Components\"); plt.subplot(133); plt.plot(U[:,0],U[:,1],'.'); plt.xlabel(\"Principle Component 1\"); plt.ylabel(\"Principle Component 2\"); plt.title(\"Interpreting Principle Components of ~X\");\n",
    "for i in range(0, U.shape[0]):\n",
    "    if all(np.sum(((U[:i,:2]-U[i,:2])**2).dot([[1],[15]]), axis=1) > .02):\n",
    "        plt.text(U[i,0],U[i,1],mtcars.data.index[i], horizontalalignment=\"right\")\n",
    "for j in range(Vt.shape[0]):\n",
    "    plt.plot([0,Vt[0,j]],[0,Vt[1,j]],'k'); plt.text(Vt[0,j], Vt[1,j], mtcars.data.columns[j], color='r')\n",
    "# Third plot interprets the \"Principle Directions\" associated with each \"Principle Component\"\n",
    "# The first \"Principle Component\" (the first column of U from the SVD) points in the direction of cyl, disp negative mpg axes\n",
    "# The elements of the first column of U are the coordinates of the data points along this direction\n",
    "# The blue points are data points, and you can see their locations relative to the Priniple Directions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8d3gU4sxjIPa",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-X-UDVt\"></a>\n",
    "\n",
    "## 5.3.A SVD Versus Eigendecomposition for PCA (or PCR) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "The ***PCA*** analyses above used an ***SVD*** computation; however <font style=\"color:gray\">(as discussed in this [stackoverflow](https://stats.stackexchange.com/questions/314046/why-does-andrew-ng-prefer-to-use-svd-and-not-eig-of-covariance-matrix-to-do-pca) conversation),</font><br>there are multiple distinct algorithms which could be used to compute $V^T$ and $D$ (and thus compute ***PCA***)\n",
    "\n",
    "- `np.linalg.svd(X)`/`np.linalg.svd(X^TX)`/`np.linalg.eig(X^TX)`/`np.linalg.eigh(X^TX)`\n",
    "\n",
    "But `np.linalg.svd(X)` is the best choice for two reasons:\n",
    "\n",
    "1. All computations generally entail ***roundoff error*** so $X^TX$ not only requires additional computation,<br>it also unneccesarily introduces numerical inaccuracy \n",
    "  - Even the ***singular values***/***eigenvalues*** $D_{ii}^2$ (of $X^TX$) tend to be less precice compared to the numerical accuracy of ***singular values*** $D_{ii}$ (of $X$) since squaring introducess the possibility for ***roundoff error***\n",
    "  \n",
    "2. The ***condition*** of $X$ for ***spectral radius*** ${\\rho(X) = \\max_i D_{ii}} > 1 > \\min_j D_{jj}$ is better than the ***condition*** of the ***gramian*** $X^TX$ with ***spectral radius*** ${\\rho(X^TX) = \\max_i D_{ii}^2} >> 1 >> \\min_j D_{jj}^2$ since\n",
    "   \n",
    "   $$\\kappa(X) = \\frac{\\max_i D_{ii}}{\\min_j D_{jj}} << \\frac{\\max_i D_{ii}^2}{\\min_j D_{jj}^2} = \\kappa(X^TX) \\quad \\text{ or } \\quad \\kappa(X^TX) = \\frac{\\lambda_{max}^2}{\\lambda_{min}^2} >> \\frac{\\lambda_{max}}{\\lambda_{min}} = \\kappa(X)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-Axb-math-pca-pcr\"></a>\n",
    "\n",
    "## 5.3.A SVD Versus Eigendecomposition for PCA (or PCR)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {
    "id": "6O4knk5SjaDw"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total variance 7.0 should match the sum of the eigenvalues\n",
      "which is also equal to the sum of squares of singular values.\n",
      "\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 7.000000000000001\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999995\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999999\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999999\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999996\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999998\n",
      "[1.43104   1.1419107 1.0709775 1.0176375 0.9354291 0.7341884 0.6688168] 6.999999999999995\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=7)\n",
    "n,m = 100,7; X = stats.norm().rvs(size=(n,m)); X = (X - X.mean(axis=0))/X.std(axis=0)\n",
    "print(\"The total variance\", X.var(axis=0).sum(), end=\" \"); print(\"should match the sum of the eigenvalues\"); print(\"which is also equal to the sum of squares of singular values.\\n\")\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix; np.linalg.eigh # \"complex Hermitian (conjugate symmetric) or a real symmetric matrix.\"\n",
    "eignvals = np.sort(np.linalg.eigh(np.cov(X.T, ddof=0))[0])[::-1]; print(eignvals, eignvals.sum())\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix # np.linalg.eig: general eigendcomposition function\n",
    "eignvals = np.sort(np.linalg.eig(np.cov(X.T, ddof=0))[0])[::-1]; print(eignvals, eignvals.sum())\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix # SVD/eigendecomposition equivalence for symmetric positive definite matrices\n",
    "eignvals = np.linalg.svd(np.cov(X.T, ddof=0))[1]; print(eignvals, eignvals.sum())\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix # np.linalg.eigh with matrix-based covariance computation\n",
    "eignvals = np.sort(np.linalg.eigh(X.T.dot(X)/n)[0])[::-1]; print(eignvals, eignvals.sum())\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix # np.linalg.eig with matrix-based covariance computation\n",
    "eignvals = np.sort(np.linalg.eig(X.T.dot(X)/n)[0])[::-1]; print(eignvals, eignvals.sum())\n",
    "# Traditional PCA: eigendecomposition of the covariance matrix # np.linalg.eig with matrix-based covariance computation\n",
    "eignvals = np.linalg.svd(X.T.dot(X)/n)[1]; print(eignvals, eignvals.sum())\n",
    "# PCA with SVD \n",
    "singvals = np.linalg.svd(X/n**0.5)[1]; print(singvals**2, (singvals**2).sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In ***PCA***, because of the generally increased ***condition number*** of the ***covariance matrix*** $ X^T  X$ relative to the scaled data matrix $ X$, applying ***SVD*** to $ X$ is more numerically stable than computing the ***eigendecomposition*** or ***SVD*** of $ X^T  X$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 5.3.A SVD Versus Eigendecomposition for PCA (or PCR)\n",
    "\n",
    "---\n",
    "\n",
    "However..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.4 µs ± 89.6 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "np.linalg.eigh(np.cov(X.T, ddof=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "31.1 µs ± 261 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.eig(np.cov(X.T, ddof=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28.2 µs ± 160 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.svd(np.cov(X.T, ddof=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.14 µs ± 12.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.eigh(X.T.dot(X)/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.6 µs ± 73.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.eig(X.T.dot(X)/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.8 µs ± 38.3 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.svd(X.T.dot(X)/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "310 µs ± 17.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\\\\ np.linalg.svd(X/n**0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-Axb-math-ica\"></a>\n",
    "\n",
    "## 5.3.B Independent Components Analysis (ICA) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "- ***Linear independence*** is not the same as ***statistical independence***\n",
    "- ***Principal components*** (columns of $U$ in $X=UDV^T$) are ***linear independent*** $\\Longrightarrow$ (empirically) ***uncorrelated***\n",
    "- The example shows that (as well as the ***principal components***) the ***principal directions*** (rows of $V^T$)  are ***linearly independent*** but elements of the ***principal components*** (the entries in the rows of $U$) are ***statistically dependent***\n",
    "\n",
    "<span style='color:white'>\n",
    "    \n",
    "***Independent Component Analysis (ICA)*** instead finds directions which may be ***linearly dependent*** but which nonetheless instead form a ***basis*** under which the data actually IS (empirically) ***statistically independent*** \n",
    "\n",
    "***PCA*** identifies sequential ***principal directions*** of maximal data variation; whereas, ***ICA*** finds directions maximizing ***kurtosis*** (***heavy tailedness***); so, ***PCA*** naturally identifies ***Gaussian covariance structure***; whereas, ***ICA*** contrarily works in the context of ***Anti-Gaussianity***... the less ***Gaussian*** the data is the better ***ICA*** can find \"pointy independent directions\"\n",
    "    \n",
    "</span>\n",
    "\n",
    "|![](https://alliance.seas.upenn.edu/~cis520/dynamic/2022/wiki/uploads/Lectures/PCA_ICA.png)|![](https://alliance.seas.upenn.edu/~cis520/dynamic/2022/wiki/uploads/Lectures/PCA_ICA.png)|\n",
    "|-|-|\n",
    "| | |\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-Axb-math-ica\"></a>\n",
    "\n",
    "## 5.3.B Independent Components Analysis (ICA) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "- ***Linear independence*** is not the same as ***statistical independence***\n",
    "- ***Principal components*** (columns of $U$ in $X=UDV^T$) are ***linear independent*** $\\Longrightarrow$ (empirically) ***uncorrelated***\n",
    "- The example shows that (as well as the ***principal components***) the ***principal directions*** (rows of $V^T$)  are ***linearly independent*** but elements of the ***principal components*** (the entries in the rows of $U$) are ***statistically dependent***\n",
    "\n",
    "***Independent Component Analysis (ICA)*** instead finds directions which may be ***linearly dependent*** but which nonetheless instead form a ***basis*** under which the data actually IS (empirically) ***statistically independent*** \n",
    "\n",
    "***PCA*** identifies sequential ***principal directions*** of maximal data variation; whereas, ***ICA*** finds directions maximizing ***kurtosis*** (***heavy tailedness***); so, ***PCA*** naturally identifies ***Gaussian covariance structure***; whereas, ***ICA*** contrarily works in the context of ***Anti-Gaussianity***... the less ***Gaussian*** the data is the better ***ICA*** can find \"pointy independent directions\"\n",
    "\n",
    "|![](https://alliance.seas.upenn.edu/~cis520/dynamic/2022/wiki/uploads/Lectures/PCA_ICA.png)|![](https://alliance.seas.upenn.edu/~cis520/dynamic/2022/wiki/uploads/Lectures/PCA_ICA.png)|\n",
    "|-|-|\n",
    "| | |\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<a name=\"cell-sovling-Axb-math-pcr\"></a>\n",
    "\n",
    "# 5.4 Principal Components Regression (PCR) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "For ***full rank*** $X_{n \\times m}$, the ***SVD*** $X=UDV^T$ produces an ***orthonormal*** $V$ so that the data point\n",
    "\n",
    "$$X_{i \\cdot} = U_{i \\cdot} DV^T \\quad \\text{ or } \\quad x_i = \\underbrace{VD}_{A}u_i$$ \n",
    "can be be represented by $U_{i \\cdot}$ in the ***orthogonal basis*** defined by the columns of $A=VD$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.9030599 -0.0222713  0.7074139] \n",
      " [-0.9030599 -0.0222713  0.7074139]\n"
     ]
    }
   ],
   "source": [
    "i=1; X = stats.norm.rvs(size=(5,3)); \n",
    "U,d,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "print(X[i,:], \"\\n\", (U[i,:]*d)@Vt) # U[i,:]*d is the \"broadcasted\" version of U[i,:]@np.diag(D) # https://numpy.org/doc/stable/user/basics.broadcasting.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Data point $X_{i \\cdot}$ is represented in the ***standard (orthonormal) basis***<br>but the columns $X_{\\cdot j}$ are not necessarily ***linearly independent*** but\n",
    "\n",
    "\n",
    "- Data point $U_{i \\cdot}$ is represented in an ***orthogonal basis***<br>and $U$ itself has ***linearly independent*** (***semi-orthonormal*** $U^TU = I_{m \\times m}$) columns $U_{\\cdot j}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<a name=\"cell-sovling-Axb-math-pcr\"></a>\n",
    "\n",
    "# 5.4 Principal Components Regression (PCR) ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "For ***full rank*** $X_{n \\times m}$, the ***SVD*** $X=UDV^T$ produces an ***orthonormal*** $V$ so that the data point\n",
    "\n",
    "$$X_{i \\cdot} = U_{i \\cdot} DV^T \\quad \\text{ or } \\quad x_i = \\underbrace{VD}_{A}u_i$$ \n",
    "can be be represented by $U_{i \\cdot}$ in the ***orthogonal basis*** defined by the columns of $A=VD$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.9030599 -0.0222713  0.7074139] \n",
      " [-0.9030599 -0.0222713  0.7074139]\n"
     ]
    }
   ],
   "source": [
    "i=1; X = stats.norm.rvs(size=(5,3)); \n",
    "U,d,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "print(X[i,:], \"\\n\", (U[i,:]*d)@Vt) # U[i,:]*d is the \"broadcasted\" version of U[i,:]@np.diag(D) # https://numpy.org/doc/stable/user/basics.broadcasting.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A point in $m$-dimensional space can be equivalently defined by different ***bases***, so rows of $X$ and $U$ represent the same collection of points under different ***bases***; but, $U$ has ***linearly independent*** columns so it has no ***multicollinearity***\n",
    "\n",
    "- ***PCA*** initially figures as an ***unsupervised learning*** methodology, but it also has an interesting use in linear regression where it can replace a ***linearly dependent*** $X$ with ***linearly independent (semi-orthogonal)*** $U$ \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1KW4HUcXiYMN",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.4 Principal Components Regression (PCR) \n",
    "\n",
    "---\n",
    "\n",
    "***Principal components*** provides a \"latent factors\" interpretation as $U$ columns are linear combinations of the original columns of $X$; namely, $x_i = VDu_i$ but where the elements of $u_i$ are empirically uncorrelated, and hence have no ***multicollinearity***...\n",
    "\n",
    "$\\hat y_i = \\beta_0 + \\beta_1 X_{i1} + \\beta_2 X_{i2} + \\beta_3 X_{i3} + \\cdots =  \\beta_0 + \\tilde\\beta_1 U_{i1} + \\tilde\\beta_2 U_{i2} + \\tilde\\beta_3 U_{i3} + \\cdots \\quad \\text{ since $X_{\\cdot j}$ and $U_{\\cdot j}$}$\n",
    "\n",
    "$U_{\\cdot j} = \\left[X  V D^{-1}\\right]_{\\cdot j} = \\sum_{k=1}^m X_{\\cdot k} V_{k j}/\\lambda_j \\quad \\text{ and } \\quad X_{\\cdot j} = \\left[U D V^T \\right]_{\\cdot j} = \\sum_{k=1}^m \\lambda_k U_{\\cdot k} [V^T]_{k j} \\quad \\text{ are linear combinations of each other...}$\n",
    "\n",
    "\n",
    "> $U$ from the ***SVD*** of $X$ or computable from $V$ and $D$ of the ***gramian*** $X^TX$ ***eigendecomposition*** \n",
    ">\n",
    ">  $$X = UDV^T \\Longrightarrow \\underbrace{XVD^{-1} = UDV^TVD^{-1} = U}_{\\text{expressed for a single data point }D^{-1}V^Tx_i = u_i}$$\n",
    ">\n",
    "> - has ***SVD*** $U=U\\Lambda W^T = U_{n\\times m}I_{m \\times m}I_{m \\times m}$ (characteristic of all ***orthogonal matrices***)\n",
    "> - so $U$ ***singular values*** $\\lambda_i = \\Lambda_{ii} = I_{ii} = 1$ and $1 = \\kappa(U)\\;$ ($<< \\kappa(X)$ ***ill-conditioned***)\n",
    "> - avoids attribution uncertainty driven variance inflaction from ***multicollinearity***\n",
    ">    - by replacing a potentially ***ill-conditioned*** $X$ with a ***perfectly conditioned*** $U$\n",
    ">    - since the ***singular values*** of $X$ have already been factored out in $UDV^T$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.4 Principal Components Regression (PCR) \n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {
    "id": "PuRAtOkgiZJU"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Model:</td>\n",
       "      <td>OLS</td>\n",
       "      <td>Adj. R-squared:</td>\n",
       "      <td>0.839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Dependent Variable:</td>\n",
       "      <td>y</td>\n",
       "      <td>AIC:</td>\n",
       "      <td>275.2616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Date:</td>\n",
       "      <td>2024-02-02 09:49</td>\n",
       "      <td>BIC:</td>\n",
       "      <td>283.0771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>No. Observations:</td>\n",
       "      <td>100</td>\n",
       "      <td>Log-Likelihood:</td>\n",
       "      <td>-134.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Df Model:</td>\n",
       "      <td>2</td>\n",
       "      <td>F-statistic:</td>\n",
       "      <td>258.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Df Residuals:</td>\n",
       "      <td>97</td>\n",
       "      <td>Prob (F-statistic):</td>\n",
       "      <td>1.30e-39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>R-squared:</td>\n",
       "      <td>0.842</td>\n",
       "      <td>Scale:</td>\n",
       "      <td>0.89154</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     0                 1                    2         3\n",
       "0               Model:               OLS      Adj. R-squared:     0.839\n",
       "1  Dependent Variable:                 y                 AIC:  275.2616\n",
       "2                Date:  2024-02-02 09:49                 BIC:  283.0771\n",
       "3    No. Observations:               100      Log-Likelihood:   -134.63\n",
       "4            Df Model:                 2         F-statistic:     258.8\n",
       "5        Df Residuals:                97  Prob (F-statistic):  1.30e-39\n",
       "6           R-squared:             0.842               Scale:   0.89154"
      ]
     },
     "execution_count": 467,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100; X = stats.multivariate_normal(cov=np.array(((1,.999),(.999,1)))).rvs(n)\n",
    "Y = 1 + X.dot(np.ones(2)) + stats.norm().rvs(n)  \n",
    "model = sm.OLS(Y,sm.add_constant(X)); results = model.fit(); results.summary2().tables[0] # scale = residual variance\n",
    "#float(results.summary2().tables[0].iloc[-1,-1])**.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {
    "id": "K_mltS7DpgQy"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coef.</th>\n",
       "      <th>Std.Err.</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "      <th>[0.025</th>\n",
       "      <th>0.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>1.065204</td>\n",
       "      <td>0.097378</td>\n",
       "      <td>10.938885</td>\n",
       "      <td>1.276737e-18</td>\n",
       "      <td>0.871936</td>\n",
       "      <td>1.258472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>0.050351</td>\n",
       "      <td>2.167678</td>\n",
       "      <td>0.023228</td>\n",
       "      <td>9.815161e-01</td>\n",
       "      <td>-4.251889</td>\n",
       "      <td>4.352591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>2.012132</td>\n",
       "      <td>2.165624</td>\n",
       "      <td>0.929123</td>\n",
       "      <td>3.551315e-01</td>\n",
       "      <td>-2.286032</td>\n",
       "      <td>6.310295</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Coef.  Std.Err.          t         P>|t|    [0.025    0.975]\n",
       "const  1.065204  0.097378  10.938885  1.276737e-18  0.871936  1.258472\n",
       "x1     0.050351  2.167678   0.023228  9.815161e-01 -4.251889  4.352591\n",
       "x2     2.012132  2.165624   0.929123  3.551315e-01 -2.286032  6.310295"
      ]
     },
     "execution_count": 469,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary2().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 472,
   "metadata": {
    "id": "qfExbNJxiZLb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(539.282932587103, 539.282932587103)"
      ]
     },
     "execution_count": 472,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VIF(X,0),VIF(X,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.4 Principal Components Regression (PCR) \n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 473,
   "metadata": {
    "id": "V3O04R2bib95"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Model:</td>\n",
       "      <td>OLS</td>\n",
       "      <td>Adj. R-squared:</td>\n",
       "      <td>0.839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Dependent Variable:</td>\n",
       "      <td>y</td>\n",
       "      <td>AIC:</td>\n",
       "      <td>275.2616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Date:</td>\n",
       "      <td>2024-02-02 09:50</td>\n",
       "      <td>BIC:</td>\n",
       "      <td>283.0771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>No. Observations:</td>\n",
       "      <td>100</td>\n",
       "      <td>Log-Likelihood:</td>\n",
       "      <td>-134.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Df Model:</td>\n",
       "      <td>2</td>\n",
       "      <td>F-statistic:</td>\n",
       "      <td>258.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Df Residuals:</td>\n",
       "      <td>97</td>\n",
       "      <td>Prob (F-statistic):</td>\n",
       "      <td>1.30e-39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>R-squared:</td>\n",
       "      <td>0.842</td>\n",
       "      <td>Scale:</td>\n",
       "      <td>0.89154</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     0                 1                    2         3\n",
       "0               Model:               OLS      Adj. R-squared:     0.839\n",
       "1  Dependent Variable:                 y                 AIC:  275.2616\n",
       "2                Date:  2024-02-02 09:50                 BIC:  283.0771\n",
       "3    No. Observations:               100      Log-Likelihood:   -134.63\n",
       "4            Df Model:                 2         F-statistic:     258.8\n",
       "5        Df Residuals:                97  Prob (F-statistic):  1.30e-39\n",
       "6           R-squared:             0.842               Scale:   0.89154"
      ]
     },
     "execution_count": 473,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# but now we use U rather than X -- same model fit accuracy scores\n",
    "U,D,Vt = np.linalg.svd(X, full_matrices=False)\n",
    "model = sm.OLS(Y,sm.add_constant(U)); results = model.fit(); results.summary2().tables[0] # scale = residual variance\n",
    "#float(results.summary2().tables[0].iloc[-1,-1])**.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {
    "id": "wx6l-7ECp_a6"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coef.</th>\n",
       "      <th>Std.Err.</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "      <th>[0.025</th>\n",
       "      <th>0.975]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>1.065204</td>\n",
       "      <td>0.097378</td>\n",
       "      <td>10.938885</td>\n",
       "      <td>1.276737e-18</td>\n",
       "      <td>0.871936</td>\n",
       "      <td>1.258472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>21.497814</td>\n",
       "      <td>0.945500</td>\n",
       "      <td>22.736972</td>\n",
       "      <td>1.194684e-40</td>\n",
       "      <td>19.621257</td>\n",
       "      <td>23.374370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>-0.440283</td>\n",
       "      <td>0.972530</td>\n",
       "      <td>-0.452720</td>\n",
       "      <td>6.517615e-01</td>\n",
       "      <td>-2.370486</td>\n",
       "      <td>1.489919</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Coef.  Std.Err.          t         P>|t|     [0.025     0.975]\n",
       "const   1.065204  0.097378  10.938885  1.276737e-18   0.871936   1.258472\n",
       "x1     21.497814  0.945500  22.736972  1.194684e-40  19.621257  23.374370\n",
       "x2     -0.440283  0.972530  -0.452720  6.517615e-01  -2.370486   1.489919"
      ]
     },
     "execution_count": 474,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# but tighter standard errors\n",
    "results.summary2().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {
    "id": "rRhqIjCGicAJ"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 1.0)"
      ]
     },
     "execution_count": 475,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# because now there's no multicollinearity, so VIFs are 1\n",
    "VIF(U,0),VIF(U,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.4 Principal Components Regression (PCR) \n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {
    "id": "oL9tnUwIikrB"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and the SVD of U=U*I*I so singular values of U are all 1\n",
    "fix,ax = plt.subplots(1,2,figsize=(18,5))\n",
    "U,D,Vt = np.linalg.svd(X, full_matrices=False); ax[0].bar(x=range(2), height=D); ax[0].set_title(\"Singular Values\"); \n",
    "U_,D_,Vt_ = np.linalg.svd(U, full_matrices=False); ax[1].bar(x=range(2), height=D_); ax[1].set_title(\"Singular Values\"); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-Axb\"></a>\n",
    "\n",
    "# 5.5 $Ax=b\\;$in a few ways that aren't$\\;A^{-1}$ ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "The `STA410_W24_Week4_Prerequesite_LinearAlgebra.ipynb` notebook demonstrates that $A^{-1}$ computation is best done as ***backward substitution*** with ***lower triangular forms*** (probably arrived at through ***Gaussian elimination***).\n",
    "\n",
    "- When unnecessary, actual $A^{-1}$ inversion is computationally wasteful... \n",
    "- At best $A^{-1}$ computations will introduce ***roundoff error*** and at worst be ***ill-conditioned*** <span style=\"color:gray\">with large $\\kappa(A^{-1})$</span>\n",
    "\n",
    "That same notebook introduced the ***Woodbury Matrix Identity*** \n",
    "\n",
    "$$(A + UCV)^{−1} = A^{−1} − A^{−1}U (C^{−1} + VA^{−1}U)^{−1}VA^{−1}$$\n",
    "\n",
    "which is trivial to invert if $A$ and $C$ are diagonal; and, it admits ***low rank*** $m<n$ matrix approximations, e.g., for $m=1$\n",
    "\n",
    "$$ \\Sigma_{n \\times n}^{-1} \\approx (I_{n \\times n} + \\mathbf{u}_{n\\times m}(\\mathbf{v}^T)_{n\\times m})^{-1} = I - \\mathbf{u}(1+\\mathbf{v}^T\\mathbf{u})^{-1}\\mathbf{v}^T = I - \\frac{\\mathbf{u}\\mathbf{v}^T}{1+\\mathbf{v}^T\\mathbf{u}} \\quad \\text{ with } A=I \\text{ and } C=1$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-svd\"></a>\n",
    "\n",
    "## 5.5.A The return of the SVD ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "The easiest inversions are for ***diagonal*** $D$ where $[D^{-1}]_{ii} = 1/D_{ii}$ and ***orthogonal*** $U$ where $U^{-1}=U^T$ \n",
    "\n",
    "\n",
    "If $A^{-1}$ exists then from the ***SVD*** $A = UDV^T$ and $A^{-1} = V D^{-} U^T$ with ***(semi-)orthogonal*** $U$ and $V$ and ***diagonal*** $D$\n",
    "\n",
    "$$x = V D^{-1} U^Tb \\quad \\text{ solves } \\quad x = A^{-1}b$$ \n",
    "\n",
    "For example, $\\hat \\beta$ solving $\\;X^TX\\hat \\beta = X^Ty\\;$ provides the ***least squares*** approximation $X\\hat \\beta \\approx  y$ is found the (unique) ***Moore-Penrose (generalized) inverse*** of $(X^TX)^+$ which follows directly from the ***SVD*** of $X = UDV^T$\n",
    "\n",
    "$$\\underset{(X^TX)^+(X^TX) = (X^TX)(X^TX)^+ = I}{(X^TX)^+ = V (D^{+})^2 V^T} \\underset{\\text{full rank}}{\\overset{\\text{if $X$ is}}{=}} (X^TX)^{-1} \\text{ with } (D^{+}_{ii})^2=\\frac{1}{D_{ii}^2} \\text{ so that } \\hat \\beta=V (D^{+})^2 V^T X^T y$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X, Y:\n",
      "[[0 0]\n",
      " [1 1]\n",
      " [2 2]] [0 1 2]\n",
      "\n",
      "(XtX)^-1:\n",
      "ERROR: Singular matrix\n",
      "'One does not simply invert a singular matrix' -- Boromir (The Lord of the Rings)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0,0],[1,1],[2,2]]); Y = np.array([0,1,2]); print(\"X, Y:\"); print(X, Y, end=\"\\n\\n\"); print(\"(XtX)^-1:\")\n",
    "try:\n",
    "    np.linalg.inv(X.T.dot(X))\n",
    "except np.linalg.LinAlgError as err:\n",
    "    print(\"ERROR:\", err); print(\"'One does not simply invert a singular matrix' -- Boromir (The Lord of the Rings)\", end='\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-svd\"></a>\n",
    "\n",
    "## 5.5.A The return of the SVD ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "The easiest inversions are for ***diagonal*** $D$ where $[D^{-1}]_{ii} = 1/D_{ii}$ and ***orthogonal*** $U$ where $U^{-1}=U^T$ \n",
    "\n",
    "\n",
    "If $A^{-1}$ exists then from the ***SVD*** $A = UDV^T$ and $A^{-1} = V D^{-} U^T$ with ***(semi-)orthogonal*** $U$ and $V$ and ***diagonal*** $D$\n",
    "\n",
    "$$x = V D^{-1} U^Tb \\quad \\text{ solves } \\quad x = A^{-1}b$$ \n",
    "\n",
    "For example, $\\hat \\beta$ solving $\\;X^TX\\hat \\beta = X^Ty\\;$ provides the ***least squares*** approximation $X\\hat \\beta \\approx  y$ is found the (unique) ***Moore-Penrose (generalized) inverse*** of $(X^TX)^+$ which follows directly from the ***SVD*** of $X = UDV^T$\n",
    "\n",
    "$$\\underset{(X^TX)^+(X^TX) = (X^TX)(X^TX)^+ = I}{(X^TX)^+ = V (D^{+})^2 V^T} \\underset{\\text{full rank}}{\\overset{\\text{if $X$ is}}{=}} (X^TX)^{-1} \\text{ with } (D^{+}_{ii})^2=\\frac{1}{D_{ii}^2} \\text{ so that } \\hat \\beta=V (D^{+})^2 V^T X^T y$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XtX:\n",
      "[[5 5]\n",
      " [5 5]]\n",
      "\n",
      "XtX from SVD:\n",
      "[[5. 5.]\n",
      " [5. 5.]]\n"
     ]
    }
   ],
   "source": [
    "U,D,Vt = np.linalg.svd(X, full_matrices=False); D = np.diag(D) #U,D,Vt = np.linalg.svd(X.T.dot(X)); D = np.diag(D); \n",
    "print(\"XtX:\"); print(X.T.dot(X), end=\"\\n\\n\")\n",
    "print(\"XtX from SVD:\"); print(Vt.T.dot(D**2).dot(Vt)) #print(((U.dot(D).dot(Vt)).T.dot(U.dot(D).dot(Vt))), end=\"\\n\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-svd\"></a>\n",
    "\n",
    "## 5.5.A The return of the SVD ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "The easiest inversions are for ***diagonal*** $D$ where $[D^{-1}]_{ii} = 1/D_{ii}$ and ***orthogonal*** $U$ where $U^{-1}=U^T$ \n",
    "\n",
    "\n",
    "If $A^{-1}$ exists then from the ***SVD*** $A = UDV^T$ and $A^{-1} = V D^{-} U^T$ with ***(semi-)orthogonal*** $U$ and $V$ and ***diagonal*** $D$\n",
    "\n",
    "$$x = V D^{-1} U^Tb \\quad \\text{ solves } \\quad x = A^{-1}b$$ \n",
    "\n",
    "For example, $\\hat \\beta$ solving $\\;X^TX\\hat \\beta = X^Ty\\;$ provides the ***least squares*** approximation $X\\hat \\beta \\approx  y$ is found the (unique) ***Moore-Penrose (generalized) inverse*** of $(X^TX)^+$ which follows directly from the ***SVD*** of $X = UDV^T$\n",
    "\n",
    "$$\\underset{(X^TX)^+(X^TX) = (X^TX)(X^TX)^+ = I}{(X^TX)^+ = V (D^{+})^2 V^T} \\underset{\\text{full rank}}{\\overset{\\text{if $X$ is}}{=}} (X^TX)^{-1} \\text{ with } (D^{+}_{ii})^2=\\frac{1}{D_{ii}^2} \\text{ so that } \\hat \\beta=V (D^{+})^2 V^T X^T y$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XtX^+ from SVD:\n",
      "[[0.05 0.05]\n",
      " [0.05 0.05]]\n",
      "\n",
      "Y, Yhat:\n",
      "[0 1 2] [0. 1. 2.]\n"
     ]
    }
   ],
   "source": [
    "Dplus2 = np.zeros(D.shape); Dplus2[0,0] = 1/D[0,0]**2; print(\"XtX^+ from SVD:\"); print(Vt.T.dot(Dplus2).dot(Vt), end=\"\\n\\n\")    \n",
    "Yhat = X.dot(Vt.T.dot(Dplus2).dot(Vt.T)).dot(X.T).dot(Y.T); print(\"Y, Yhat:\"); print(Y, Yhat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-chol\"></a>\n",
    "\n",
    "## 5.5.B The Cholesky ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "If ***condition number*** $\\kappa(X^TX)$ isn't large then $X^TX$ has minimal ***roundoff error*** and ***full rank*** $X_{n \\times m}$ means $(X^TX)_{m \\times m}$\n",
    "\n",
    "- is ***symmetric full rank***, so it has ***positive eigenvalues***, so it's ***positive definite*** with $x^TX^TXx > 0$\n",
    "\n",
    "***Symmetric*** $\\Sigma = \\Sigma^T$ and ***positive definite*** $x^T\\Sigma x > 0$ has a ***Cholesky decomposition*** \n",
    "\n",
    "$$\\Sigma = CC^T \\quad \\text{with lower triangular }C \\text{ (which is unique when $C_{ii} >0$)}$$\n",
    "\n",
    "so $\\hat \\beta$ solving $\\;X^TX\\hat \\beta = X^Ty\\;$ providing the ***least squares*** approximation $X\\hat \\beta \\approx  y$ can be solved for as\n",
    "\n",
    "$$\\begin{align*}\n",
    "X^T\\!X\\hat \\beta = X^T\\!y \n",
    "= CC^T \\hat \\beta = {} & X^T\\!y \\\\\n",
    "\\Longrightarrow  \\text{ by solving for $\\gamma$ in } \\underset{L}{C} (\\underbrace{C^T \\hat \\beta}_{\\gamma}) = {} & X^T\\!y \\; \\text{ and then $\\hat \\beta$ in} \\; \\underset{U}{C}^T \\hat \\beta = \\gamma \\quad \\text{using }\\textbf{backward substitution}\\text{ }\\\\{}\n",
    "  \\end{align*}$$\n",
    "\n",
    "- A ***Cholesky decomposition*** algorithm is considered in `STA410_W24_Week5_Extra_LinearAlgebraAlgorithms.ipynb`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-chol-mvn\"></a>\n",
    "\n",
    "## 5.5.C Multivariate Normal ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "***Cholesky decomposition*** $\\Sigma=CC^T$ and ***LU decomposition*** $\\Sigma=LU$ algorithms are both $O(n^3)$ but the ***Cholesky***\n",
    "\n",
    "- is constructed with half of as many operations\n",
    "- requires $n(n+1)/2$ elements, half of the $n^2+n$ elements stored in ***LU decomposition*** since $C$ is repeated\n",
    "\n",
    "- is twice as fast to ***invert*** since $(CC^T)^{-1} = (C^T)^{-1}C^{-1} = $ [$ \\;(C^{-T})C^{-1}$](https://math.stackexchange.com/questions/340233/transpose-of-inverse-vs-inverse-of-transpose) $= (C^{-1})^TC^{-1}$  only requires the computation of $C^{-1}$ while $(LU)^{-1} = U^{-1}L^{-1}$ requires both $L^{-1}$ and $U^{-1}$\n",
    "\n",
    "<!-- and so the ***Cholesky decomposition*** is an interesting exception to the typical ***time-space tradeoff*** since its construction outperforms ***LU decomposition*** both in computation *and* memory requirements. For additional details and commentary on ***Cholesky decomposition***, please see Keith Knight's STA410 [notes7.pdf](https://q.utoronto.ca/courses/296804/files?preview=24300633) document beginning on page 13 and [notes9.pdf](https://q.utoronto.ca/courses/296804/files?preview=24301088) beginning on page 37. -->\n",
    "\n",
    "$$\\text{Further }\\quad \\mathbf{Y} \\sim MVN(\\mathbf{0},\\mathbf{I}) \\quad \\Longrightarrow \\quad C Y \\sim MVN(\\mathbf{0}, \\boldsymbol \\Sigma=CC^T)$$\n",
    "\n",
    "$$\\text{so to evaluate }\\quad \\displaystyle (2\\pi )^{-k/2}\\det({\\boldsymbol {\\Sigma }})^{-1/2}\\,\\exp \\left(-{\\frac {1}{2}}(\\mathbf {Y} -{\\boldsymbol {\\mu }})^{\\mathrm {T} }{\\boldsymbol {\\Sigma }}^{-1}(\\mathbf {Y} -{\\boldsymbol {\\mu }})\\right)$$\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    "(\\mathbf {Y} -{\\boldsymbol {\\mu }})^{\\mathrm {T} }{ { [C C^T] }}^{-1}(\\mathbf {Y} -{\\boldsymbol {\\mu }}) = \n",
    "[(\\mathbf {Y} -{\\boldsymbol {\\mu }})^{\\mathrm {T} } C^{-T}] C^{-1} (\\mathbf {Y} -{\\boldsymbol {\\mu }}) = {} & b\\\\\n",
    "[C^{-1}(\\mathbf {Y} -{\\boldsymbol {\\mu }})]^{\\mathrm {T} } C^{-1} (\\mathbf {Y} -{\\boldsymbol {\\mu }}) = {} & b \\;\\; \\Longrightarrow \\;\\; \\underbrace{\\textbf{z}^T\\textbf{z} = b}_{\\textbf{z} = C^{-1} (\\mathbf {Y} -{\\boldsymbol {\\mu }})} \\;\\;  \\underbrace{ \\Longrightarrow \\;\\;  C\\textbf{z} = \\mathbf {Y} -{\\boldsymbol {\\mu }}}_{\\text{solve for $\\textbf{z}$ compute $\\exp(\\textbf{z}^T\\textbf{z})$}} \\\\\n",
    "\\det(\\boldsymbol {\\Sigma }) = \\underbrace{\\det(CC^T) = \\det(C)\\det(C^T)}_{\\text{produces and trangular matrices are easy}} =  & {} \\prod_i C_{ii} \\prod_i C_{ii}^T = \\prod_i C_{ii}^2\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-mvn\"></a>\n",
    "\n",
    "## 5.5.D Square Root Decomposition ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "***Cholesky decomposition*** is sometimes referred to as the ***square-root decomposition***...<br> but for ***symmetric nonnegative definite*** $A$ the ***square-root decomposition*** is already defined based on ***diagonal*** $D$ and ***orthogonal*** $V$ as\n",
    "\n",
    "$$A^{\\frac{1}{2}} = VD^{\\frac{1}{2}}V^T \\quad \\text{ such that } \\quad \\left(A^{\\frac{1}{2}}\\right)^2= VDV^T = A$$\n",
    "\n",
    "***Square-root decomposition*** often proves useful in theoretical settings<br> whereas the computational efficiencies of ***Cholesky decomposition*** lead to its ubiquity in applied settings\n",
    "\n",
    "> The ***singular values = eigenvalues*** in ***PCA*** $X^TX=UDV^T = VDV^T$ <br>provide a ***square-root decomposition*** \n",
    ">\n",
    ">  $$(X^TX)^{\\frac{1}{2}} = VD^{\\frac{1}{2}}V^T$$\n",
    ">\n",
    ">  where $D^{\\frac{1}{2}} = \\tilde D$ are the ***singular values*** from $X = \\tilde U \\tilde DV^T$  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-qr\"></a>\n",
    "\n",
    "## 5.5.E $QR$ Decomposition ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "***(Modified) Gram-Schmidt procedure*** processes $X$ into a ***linearly independent*** columns that can be ***normalized*** as $Q$\n",
    "\n",
    "- ***(Modified) Gram-Schmidt procedure*** details are addressed in `STA410_W24_Week5_Extra_LinearAlgebraAlgorithms.ipynb`\n",
    "\n",
    "Column $j$ of $Q$ is a linear combination of the first $j$ columns of $X$ so for some ***upper trapezoidal matrix*** $R$\n",
    "\n",
    "$$X = QR \\quad \\text{ with }\\textbf{(semi-)orthonormal } {Q_{\\cdot j}^TQ_{\\cdot j'} = \\left\\{\\begin{array}{l}1: \\text{if } j=j' \\quad  \\text{i.e., the columns are normal vectors}\\\\0: \\text{if } j\\not=j'  \\quad \\text{i.e., the columns are orthogonal}\\end{array}\\right.}$$\n",
    "\n",
    "The ***QR decomposition*** is ***rank revealing*** when $X$ is not ***full rank***, since ***linearly dependent*** produce $\\mathbf{0}$ column vectors\n",
    "\n",
    "$$\\overset{\\text{rank } r}{X_{n\\times m}} = \n",
    "\\overset{\\text{orthonormal}}{\\left[\\overbrace{Q_{n\\times r}}^{\\text{semi-}} \\; \\Big | \\; \\mathbf{0}_{n\\times (n-r)}\\right]}_{n \\times n} \\overset{\\text{trapezoidal}}{\\left[\\begin{array}{c}R_{r\\times m}\\\\\\mathbf{0}\\end{array} \\right]}_{n \\times m} = \\;\\;\\;Q_{n\\times r}R_{r\\times m}$$\n",
    "\n",
    "- $Q$ can be even more precisely calculated using ***Householder transformations*** (or ***reflections***); or, using ***Givens transformations*** (or ***rotations***) which are especially efficient if the data arives from memory row by row\n",
    "\n",
    "<!-- As noted beginning on page 39 of Keith Knight's STA410 [notes9.pdf](https://q.utoronto.ca/courses/296804/files?preview=24301088) document, even though the ***(modified) Gram-Schmidt procedure*** is more numerically precise that the original ***Gram-Schmidt procedure***, the $Q$ matrix can be even more precisely calculated using ***Householder transformations*** (or ***reflections***); or, using ***Givens transformations*** (or ***rotations***), which are especially efficient if the data arives from memory row by row. -->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-sovling-qr\"></a>\n",
    "\n",
    "## 5.5.E $QR$ Decomposition ([Return to TOC](#cell-solving))\n",
    "\n",
    "---\n",
    "\n",
    "***(Modified) Gram-Schmidt procedure*** processes $X$ into a ***linearly independent*** columns that can be ***normalized*** as $Q$\n",
    "\n",
    "- ***(Modified) Gram-Schmidt procedure*** details are addressed in `STA410_W24_Week5_Extra_LinearAlgebraAlgorithms.ipynb`\n",
    "\n",
    "Column $j$ of $Q$ is a linear combination of the first $j$ columns of $X$ so for some ***upper trapezoidal matrix*** $R$\n",
    "\n",
    "$$X = QR \\quad \\text{ with }\\textbf{(semi-)orthonormal } {Q_{\\cdot j}^TQ_{\\cdot j'} = \\left\\{\\begin{array}{l}1: \\text{if } j=j' \\quad  \\text{i.e., the columns are normal vectors}\\\\0: \\text{if } j\\not=j'  \\quad \\text{i.e., the columns are orthogonal}\\end{array}\\right.}$$\n",
    "\n",
    "When $X=QR$ is ***full rank*** $R$ will be an ***upper triangular (full rank) matrix*** so that\n",
    "$\\hat \\beta$ solving $\\;X^TX\\hat \\beta = X^Ty\\;$ providing the ***least squares*** approximation $X\\hat \\beta \\approx  y$ can be immediately solved for using ***backward substitution*** on\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "X^TX \\hat \\beta = & X^T y \\\\\n",
    "\\Longrightarrow R^TR \\hat \\beta = & R^TQ^T y\\\\\n",
    "\\overset{(R^T)^{-1} \\text{ exists}}{\\quad \\quad \\Longrightarrow} R \\hat \\beta = & Q^T y\n",
    "\\end{eqnarray*}\n",
    "\n",
    "leading to the [general advice](https://www.quora.com/Is-it-better-to-do-QR-Cholesky-or-SVD-for-solving-least-squares-estimate-and-why) to solve for $\\hat \\beta$ via ***QR decomposition*** rather than computing $X^TX$\n",
    "\n",
    "\n",
    "<!-- \n",
    "\n",
    "***QR Decomposition*** can also speed up solving ($n>m$) ***overdetermined*** (but ***consistent***) $A_{n \\times m}x=b$ (as opposed to $Ax\\approx b$) whenever $\\text{rank}(A) =r << m$ since \n",
    "\n",
    "$$A_{n \\times m}x = \\left[Q_{n \\times r}|Q_{n \\times (m-r)}'\\right] \\left[\\begin{array}{c}R_{r\\times m}\\\\\\mathbf{0}\\end{array} \\right] x=b \\quad \\text{ so } \\quad \\left[\\begin{array}{c}R\\\\\\mathbf{0}\\end{array} \\right]x = \\left[\\begin{array}{c}Q^T\\\\ Q'^T\\end{array} \\right] b$$\n",
    "\n",
    "and (when $A_{n \\times m}x=b$ is indeed ***consistent***)\n",
    "\n",
    "$$R_{r\\times r} \\overbrace{\\left[\\begin{array}{c}\\tilde x_{r\\times 1}\\\\\\mathbf{0}\\end{array} \\right]}^{x} =  \\overbrace{\\left[\\begin{array}{c} Q^T_{r \\times n} b_{n\\times 1}\\\\\\mathbf{0}\\end{array} \\right]}^{Q^Tb} \\quad \\text{ so } \\quad R_{r \\times r} \\tilde x = Q^Tb$$\n",
    "\n",
    "and this is a very small ***backward substitution*** compared to $L_{n \\times n}^{-1} A_{n \\times m}x = U_{n \\times m}x = L_{n \\times n}^{-1}b$.\n",
    "\n",
    "So even though $O(n^2m)$ ***QR decomposition*** will be about 5 times slower than ***Gaussian*** elimination (as seen above), this disadvantage may be made up for during the ***backward substitution*** step where $O(r^2)$ can be substantially faster than $O(nm)$.  And, actually, the general solution to an ***overdetermined*** system is to use the ***pseudoinverse*** available from ***SVD***. \n",
    "\n",
    "n = 1000\n",
    "A, b = stats.norm.rvs(size=(n,n)), stats.norm.rvs(size=(n,1))\n",
    "\n",
    "%timeit np.linalg.qr(A)\n",
    "\n",
    "%timeit np.linalg.solve(A,b)\n",
    "\n",
    "n,m = 2000,10\n",
    "X, y = stats.norm.rvs(size=(n,m)), stats.norm.rvs(size=(n,1))\n",
    "y = X[:,0]+X[:,1]\n",
    "\n",
    "%timeit Q,R = scipy.linalg.qr(np.tile(X,100)); np.linalg.solve(R[:10,:10], (Q.T@y)[:10])\n",
    "\n",
    "# np.linalg.lstsq(X,y, rcond=None)\n",
    "# https://stats.stackexchange.com/questions/240573/how-does-numpy-solve-least-squares-for-underdetermined-systems\n",
    "%timeit np.linalg.lstsq(np.tile(X,100),y, rcond=None)\n",
    "# Actually, numpy doesn't do an LU decomposition / Guassian elimination approach\n",
    "# rather, it uses SVD; still, this maintains a larger memory footprint than QR\n",
    "# https://math.stackexchange.com/questions/3252351/when-solving-a-linear-system-why-svd-is-preferred-over-qr-to-make-the-solution\n",
    "-->\n",
    "\n",
    "<!-- \n",
    "- The use of the ***QR decomposition*** for estimating a least squares linear model fit will be considered further in [Programming Portfolio Assignment 1 Problem 2](#cell-solving-start). \n",
    "-->\n",
    "\n",
    "<!-- a very interesting point to follow up on with Cholesky... could cholesky work?? can add this to the homework... -->\n",
    "<!-- https://www.quora.com/Is-it-better-to-do-QR-Cholesky-or-SVD-for-solving-least-squares-estimate-and-why -->"
   ]
  }
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